Terraria

QUICK SOLUTION


I will assume you are going for this after completing all other achievements and have exceptional gear and all NPCs. See my other solutions for hints on crafting stations, getting NPCs, slaying bosses, etc. I will also assume you know how to duplicate (if not see below).

The achievement requires you cover 50% of the world in Hallow/Corrupt blocks. Mud, Snow, Ash, Open Sky, etc. cannot be turned Hallow/Corrupt. The only blocks that can be Hallow/Corrupt are Dirt, Stone, and Sand! The Hallow and Corruption spread on their own in Hard Mode. Corruption moves slightly faster. This is the fastest and most efficient way to get this achievement.

DUPLICATING METHOD


HALLOW or CORRUPT
1. Start a new Small world if you do not have one or be prepared to terraform your current world. Grab some friends to help or be prepared to spend many hours working on this.
2. Build a housing structure in the sky close to the initial spawn area. I suggest using bricks and make the outer walls two bricks thick. Kill any boss to get the Dryad to move in. You will need her to check on your progress.
3. From this, build a Hellevator and a Skyvator. This is easiest by duplicating Dynamite or using Rocket IV from a Rocket Launcher to blow out a path straight down.
4. Fall down the Hellevator and kill The Wall of Flesh to unlock Hard Mode. (Optional)Then kill a Mechanical boss to get the Steampunker to spawn so you can buy clentaminators and solution.
5. Get a clentaminator and lots of solution (Purple for Corruption and Blue for Hallow).
6. Drop down the Hellevator and spray to the left.
7. Drop down the Hellevator and spray to the right.
8a. Make other shafts using the same method as the Hellevator and repeat 6 & 7 to spread the Hallow/Corruption all over under the ground. Check with the Dryad when you are finished to see how much percentage the world is Corrupt/Hallow
8b. You can dig across horizontally from the Hellevator and spray up and down, but this takes much longer.
NOTE: At this point, you can idle boost and let the Hallow/Corruption spread as far as it can reach, but bear in mind that Corruption cannot spread to Hallow or Crimson and Hallow cannot spread to Corruption or Crimson. It is also unlikely that enough will spread to get the world to 50%.
9. Go up to the top of the world using your Skyvator and build a brick bridge across the world. Build a similar one out from the housing structure.
10. Duplicate Pearlsand for Hallow or Ebonsand for Corruption and fill lots of chests.
11. Drop sand from the bridge to fill in the area between the bridge across the top of the world and the lower bridge you built. Keep in mind that NPCs cannot live in the Corruption, so for Corrupting, you will want to place the sand far enough away from the building to not affect them. Pearlsand can be placed right next to or all around your NPC structure. Sand is recommended because it falls when there is nothing under it and you can hold down to place it continuously.
MNRussell said:12. Continue checking in with the Dryad until you get to 50% Corruption/Hallow.
This is the fastest and most efficient way to get this achievement.

If you have any notes, let me know and I will add them with credit before you vote negatively.

There seems to be some confusion as to how this achievement should be unlocked and most of the other guides mention some highly inefficient methods.

Below I will outline everything you need to do to obtain this achievement within half an hour, with its counterpart only taking an additional 15 minutes.
To clarify, you only need to Corrupt / Hallow 50% of the world to unlock the respective achievements.

This guide assumes that you have already acquired the Clentaminator / Terraformer and the necessary solutions to Corrupt and Hallow your world. For those who don't, I will briefly explain how to acquire each item necessary for completing the achievement:

Drill Containment Unit - Hands down the best drill in the game, this will make digging each hellevator (A hole straight to the bottom of the world) incredibly fast.
You can craft it by combining 40 of each of the following bars at a Mythril or Orichalcum Anvil:
Luminite Bars, Chlorophyte Bars, Shroomite Bars, Spectre Bars, Hellstone Bars and Meteorite Bars.

Clentaminator - Purchased from the Steampunker for two Platinum Coins.

Terraformer - An upgraded version of the Clentaminator that is acquired by throwing the Clentaminator into the Shimmer. If possible you should aim to acquire this beforehand as it is much more efficient than the Clentaminator.

Purple Solution - Used to spread the Corruption, it can be acquired from the Steampunker for 22.5 Silver Coins per bottle whenever there is a Blood Moon or Solar Eclipse in a Corrupted world.

Blue Solution - Used to spread the Hallow, it can be acquired from the Steampunker for 22.5 Silver Coins per bottle when speaking to the Steampunker in the Hallow.

Soaring Insignia - An incredibly useful item that enables infinite flight and will allow you to quickly return to the surface after drilling a hellevator. It can be acquired from Treasure Bags dropped by the Empress of Light in Expert or Master mode (The difficulty can be adjusted at will in Journey mode).
If you don't have access to the Soaring Insignia, a Magic Mirror, Cellphone, Shellphone or Recall Potions are great alternatives to quickly teleport to the surface.

Celestial Starboard - A hoverboard that allows infinite flight and the ability to hover in place. This is a great alternative to the Soaring Insignia. It can be acquired from Treasure Bags dropped by the Moon Lord in Expert or Master mode (The difficulty can be adjusted at will in Journey mode).

This is considerably easier in Journey mode as you can speed up time to allow faster passive spread. You can also enable god mode and turn off enemy spawns which allows you to ignore all forms of danger and just focus on the two achievements. Additionally, you will be able to easily duplicate the solutions purchased from the Steampunker, giving you unlimited ammo.

Now, without further ado, lets begin:

Start off by creating a new world with the size set to small and the evil to Corruption.
Create a hellevator and kill the Wall of Flesh
Dig an additional seven hellevators that are spread out along the surface (using the mini-map as a reference, you shouldn't be able to see the previous hellevator on the mini-map when you start digging the next hellevator).
Starting from one edge of the map, aim the Terraformer straight down and spray the entire surface until you reach the other side of the map.
Return to the first hellevator and drop down it, spraying one side as you go. On the way back up the hellevator you should spray the other side.
Repeat the previous step for the other seven hellevators.
Save and Exit
Once you reload the world the achievement should unlock (if it doesn't, dig another hellevator and spray both sides before saving and exiting again. Repeat until the achievement unlocks).
With the first achievement done, you can now work on its counterpart which will go by much quicker as all of the hellevators have already been dug.

I will just clarify some incorrect information I have seen in other guides here:

Firstly, you don't need to speak to the Dryad to trigger the achievement or even have her in your world at all.

Secondly, there is no reason to place any additional blocks as only the worlds existing blocks count against you. The game doesn't take into account any blocks that cannot be corrupted or hallowed (such as ores, wood and snow).

Thirdly, the game won't update your progress until you save and exit, this is likely a glitch. As a result, you should make sure to do this after the surface and eight hellevators have been sprayed. As mentioned above, if the achievement doesn't pop, just dig another hellevator and try again.

Fourth, similarly to the above, the Dryads percentage doesn't seem to update until you save and exit... So don't rely on her to monitor progress if she is in your world.

Fifth, you CAN earn the Corruptible achievement in a Crimson world, but you won't be able to purchase the Purple Solution in the same world as it must be purchased in a world that started off with Corruption.

Sixth, this achievement can, to my knowledge, only be unlocked by the host. As such, there is no way to quickly boost this achievement as each player must create a world with 50% Corruption / Hallow themselves.

Seventh, when digging the hellevators you should start by digging a hole going straight down, the second hole however should be dug going straight up. This will save time returning to the surface and is also much quicker as any liquids (Honey, water and lava) will simply drop by you and barely slow you down. Alternating digging the holes from the surface and underworld will significantly speed up your progress.
It is worth noting that some liquids, such as water and lava, may end up combining into obsidian as they fall at different speeds. If this happens you will need to destroy these blocks on your way down later on, but it is only a minor inconvenience considering the time saved from digging a hole straight up.

Lastly, if you've made it this far, thank you for reading. I'd also be more than happy to provide the mentioned items to you so you can get started straight away. A Journey character is required.

As someone who got this achievement in the 360 version and spent a week doing so, I'm happy to say that the Journey Mode added to the 1.4 update has made this achievement much, much easier! The Hallow is slightly more difficult to spread than corruption, but this should still be easy!

If you already have a Journey character and have access to the Clentaminator plus some Green and Blue Solution to use in it, you're basically ready to go, and I'll give a simple solution first.
If you haven't played a Journey character before I'll go into more detail further down about how to get started as you'll need to do some setup before getting to working on this achievement.
It's totally fine to use any of the Journey mode options you like including God Mode, you will be able to unlock achievements even with all options turned on.

So first, here's the basic rundown:
*Be in a small world which is after the Wall of Flesh but before Plantera
*Have a Clentaminator with Green and Blue Solution
*Make your way from one side of the surface to the other spraying Blue Solution into the ground and at any other block you see (including the bottom of the ocean on each side). Make sure to remove as much Corruption or Crimson as possible
*In the Journey Mode options, turn on 24x speed in the Time option
*Dig "Hellevators" in different areas of your world, jump down them and spray your Blue Solution in a circle as you fall to spread Hallow
**Optional* Place any Hallowed blocks and normal stone/sand blocks you mined when making your hellevator in the underworld. Put them together in large blocks to help keep your Hallow% high
*When you feel you have covered a lot of the world with Hallow, save and quit, then reload and speak to the Dryad. Hopefully the achievement will pop!
*If you didn't get the achievement, check your Hallow% with the Dryad. If it's still 20-30%, you need to dig more hellevators. If it's 40% or higher, go to sleep in a bed to make time pass even quicker (you should still have the 24x speed active from earlier as well). This will make the Hallow spread on its own extremely quickly. After a while, Save/quit then speak to the Dryad again.


Now for the detailed version!

Journey Mode
Journey Mode is a new game mode introduced in the 1.4 update which allows you to do many things which will make this achievement so much easier. Unfortunately you will have to create a brand new character and world as you cannot use a non-Journey character in a Journey world. However, it's more than worth it. You can make yourself completely invincible with God Mode, make unlimited copies of any item with the Research and Duplicate function, control enemy spawns, control how quickly time passes and more. Using these tools will not affect unlocking achievements so feel free to use as many as you like.

Your main goal is to get far enough in the game to get the Steampunker to appear in your world and buy a weapon called the Clentaminator from her. You also want access to Green Solution and Blue Solution which the Clentaminator will use as ammo.
How you get to that point is up to you, it can be slow going at the beginning but with the many options available to you it won't be difficult. I would advise not spreading Hallow in your first Journey world, keeping it normal means that you can go back to get extra items or NPCs whenever you want. I personally got my first world to a point just after Plantera so I had access to good digging tools to use in my Hallow world. Getting a brand new world to a point ready for spreading Hallow will only take a few minutes for a geared-up character.

The Dryad
To unlock this achievement, you need to speak to the Dryad when she considers the world to have more than 50% of the world converted to Hallow-type blocks. This means that the Dryad must be available to speak to in your world, so it's worth making some housing early on to house her (4-5 houses should do it, you can't always control who moves in first, and the Guide and Merchant will always take the first 2 houses).
Houses count as valid even within the Hallow, so you don't need to worry about houses becoming unusable like you would in a corruption world.
The Dryad will only appear once you beat one of the early bosses - The Eye of Cthulhu, The Eater of Worlds or Skeletron. The easiest to get is probably Skeletron because all you need to do is speak to the old man outside the dungeon at night. Even if you have lousy equipment, you can use the God mode option to win.
*A final note on the Dryad, her information on the current % of Hallow in the world is not real-time and does not appear to update very often. You can force her to update her info by doing a save/quit and then reloading. I personally had her go from around 40% to over 60% by doing this.

The Steampunker
You will need to get the Steampunker to appear in order to get the Clentaminator. She will only appear once you defeat one of the mechanical bosses (The Destroyer, The Twins or Skeletron Prime). There are items available to summon them, but these are only craftable once you have beaten one of them, otherwise they are a very rare drop from any Hardmode enemy. So, the easiest thing to do is to speed up time with the Journey time option, every night at 7:30pm there is a chance one of the three bosses will spawn. You'll see a message at the bottom of the screen such as "This is going to be a terrible night.." and then after about a minute and a half real time the boss will spawn. You need to defeat them before dawn at 4:30am, although you can freeze time if you need longer. Once one of the bosses is defeated the Steampunker should move into one of your empty houses in a day or so.

The Clentaminator
As mentioned before, The Steampunker sells the Clentaminator, which is a flamethrower-like weapon. However, instead of causing damage to enemies it changes the biome of blocks depending on the colour of the Solution you load it with. For this achievement, we're interested in Green Solution which will clear any biome from a block and Blue Solution which will create Hallow on blocks. Do not get confused with Dark Blue Solution which will spread Mushroom biome instead. However, the Steampunker does not sell this Solution so it shouldn't be a problem.
The Steampunker will sell Green Solution by default, so you can buy some when you pick up the Clentaminator. The Blue Solution is slightly more tricky, as the Steampunker will only sell it if she lives within a Hallow area. Just build a small house in the Hallow and force the Steampunker to move there via the housing interface. Move away from the area, and hopefully the Steampunker will teleport to her new house where she should sell the Blue Solution.
Make sure to fully research and duplicate the two solutions so that you effectively have infinite ammo.

The Hallow
So how does the Hallow spread work exactly? It depends at what point in the game your world is. At the beginning Hallow doesn't exist at all, but if you bring the Clentaminator into a new world you can begin to spread it yourself. It will only slowly spread through grass, so you won't notice much growth. Once you beat the Wall of Flesh however, another large section of Hallow is created and it gains the ability to spread much more easily. It will now additionally infect Stone, Ice, Sand, Hardened Sand and Sandstone. Once infected, any of these blocks are able to spread to another within a 7x7 square of that tile, so it doesn't even have to be right next to a "pure" tile to be able to infect it.
When spreading Hallow, it's worth focusing first on any desert and the ocean floor. As you see above, all forms of sand can be infected so it's very good at spreading Hallow. At the other end, only ice can spread Hallow, snow does not. That means ice biomes are much harder to infect. It's worth leaving the underground ice biome till last, hopefully you can mostly ignore it. It's also more difficult to spread Hallow in the Jungle as while you can manually convert it it won't spread naturally like Corruption does because Hallow is unable to convert mud to dirt by itself. You'll need to be much more hands on in the Jungle. The Mushroom biome is totally immune to all types of spread, so if you come across one you can use the Green Solution to turn it back to ordinary blocks, then use the Blue to convert it. None of the blocks in the Underworld can be converted so can be ignored.
You will also want to make sure to cover any Corruption/Crimson which exists at the beginning and any spawned when you beat the Wall of Flesh, as this will also spread and will undo some of your work.
Once you beat Plantera, the speed of the spread of Hallow is reduced by 50%, that's why you want your world state to be between the Wall of Flesh and Plantera for this achievement.

Hellevators
A Hellevator is simply a long vertical tunnel which goes from the surface all the way down into the Underworld. You'll be needing to use these to spread Hallow through the world, by falling through them while using your Clentaminator in a circular motion all the way down. This will obviously take a lot of digging, so you'll want to use a fast digging tool, I would recommend at least a cobalt or palladium drill. I personally spent the extra time on my first world to craft the Shroomite Digging Claw, but this isn't essential by any means.

And that should just about cover everything! From the point where you have the Clentaminator, Solutions and good digging tool it should take less than an hour to get to 50% Hallow, even when starting from a brand new world. Good luck!

Here is a video but it's not mine that I found pretty useful.