Minecraft: Xbox 360 Edition

In this video I show you how to setup and defeat an Elder Guardian in the Tutorial world (make sure you never put your world on peaceful)

The Elder Guardians coordinates in the tutorial world are X:-297, Y:63, Z:319
(props to mer0u1)


*You know need milk to fight the affects caused by the guardian, more info in the comments*

CRAWFORD696's solution has the current location of the monument in the Tutorial World: X: 278 and Z: -105. Unfortunately the other guides have become outdated. This solution is how to find and kill the Elder Guardian as of the Update Aquatic.

Preparation

Start up the Tutorial World. Hit B on all the prompts and run up the wooden bridge, which will take you into an agricultural area. To your left is a house with a villager and an anvil; grab the bucket of lava from the chest outside.

Keep following the path in the direction you came from and you'll be in a huge area with deep water in the middle and cliffs and rooms all around; you should be familiar with this area if you've worked on other achievements.

Jump into the water and start punching stalks of kelp. Get a lot (maybe two stacks worth) then go up to one of the furnaces on the surface, Use the lava for fuel and cook the kelp; make sure to take the empty bucket back for later. One of the chests at water level has a fishing pole; it's probably worth getting a few fish and cooking those as well. The cooked kelp will be good for keeping your stamina up on the way to the Elder Guardian, while the cooked fish and the steak you spawned with will be good for keeping it up during the fight, since they restore you faster.

On the right side of this area is a pond with some fish, and a chest nearby. Grab all the tridents from the chest, and use one to skewer a pufferfish from the pond. Pick up the trident and the pufferfish, then head to the opposite side and find the room with brewing stands. Fill up three bottles with water, then grab Blaze Powder and Nether Wart. Brew a potion using Blaze Powder as fuel Nether Wart and Puffer Fish as ingredients to get three water breathing potions that will last for three minutes each.

Go back to the agricultural area and fill up your bucket with milk by using it on one of the cows. You should also make or find a sword and pickaxe. At least iron is preferred. Also grab a few boats from one of the chests near the water level.

Finding and Killing the Elder Guardian

Go up to the left side of the water area, following the wing signs. Grab the pair of wings from the chest, then climb up the ladder. Instead of jumping off the platform at the top and back into the water, head out the other way. Climb up on top of a tree, then use the wings to fly down into the water. Pull out a boat and the map you spawned with; you should be fairly close to the location of the monument. Use the map to find your way.

When you approach the monument, you'll get a mining fatigue effect. Navigate until you're just above the monument, and ignore all the regular Guardians as you get out of you boat. Drink the milk to remove the effect, then quickly mine just one block off the top of the monument, giving you a hole to the top room.

Take one of your water breathing potions, and start using the tridents to take pot shots at the Elder Guardian through the hole. He may clip through the monument, but hits to his clipped parts won't count, so shoot through the hole. Once you're out of tridents, go inside and chase him down with your sword. You should make quick work of him and pop your achievement.

Credit to both of the other solutions, I just wanted to add that after the last update the tutorial worlds Guardian Temple has been relocated to X: 278 and Z: -105. Hopefully this helps out anyone doing these achievements later on.

As BiLLzuMaNaTi says:
The Elder Guardians coordinates in the tutorial world are X:-297, Y:63, Z:319
(props to mer0u1)

SchiZoPHreNiikz says that you should leave the world on Easy and never switch to Peaceful, as this can mess with the spawning mechanism for the Elder Guardian.

Start a new tutorial. Stock up on food from the agricultural and livestock areas, so you don't run out. Gather wood, craft your basic tools and then craft the tools you need to mine what's required and kill the elder guardian. The Elytra tower's diamond rings can be mined for the diamond needed for your armor and sword. There's also diamond under the beacon. The underside of the beacon also contains a chest with 5 iron ingots. This is more than enough for you to build the iron pickaxe needed to mine the diamond.

Go to these locations detailed in Mist Lily's guide for Free Diver to craft the water breathing potion, which will allow you to stay under water for longer if more time is needed to kill the Elder Guardian and collect its drops.

Fishing Hole at: X: -57, Y: 78, Z: -70.
Potion Brewing area at: X: 6, Y: 79, Z: -40.

At the fishing hole, grab a fishing pole from the frame and cast the line. Once bubbles move towards the line, and you see something tug on it, pull the line out. This gives you fish or a different item. After a few tries, you'll get a Puffer Fish.

At the Potion Brewing area, fill one glass bottle from the with water and place it in the brewing stand along with Blaze Powder, which is the fuel. Add Nether Wart and the Puffer Fish one by one and recieve your 3 minute Potion of Water Breathing.

Use a boat to quickly move across the water to the Elder Guardian's location and kill it. Once you kill it, you'll unlock this achievement.