Minecraft: Xbox 360 Edition

To create the most powerful level of Beacon, you must first craft a Beacon, which is made using 5 pieces of Glass, 3 Obsidian, and 1 Nether Star, which is acquired by killing the Wither. After getting the block, you must place it atop a pyramid consisting of 4 levels of blocks, the bottom layer being 9 x 9, the next 7 x 7, then 5 x 5, and the Beacon sits on top of the middle of the next 3 x 3 layer. This pyramid can be created out of any of the valuable blocks, so Diamond Blocks, Gold Blocks, Iron Blocks, and Emerald Blocks are all acceptable for this.

The pyramid also does not require any consistency so you can use any of the 4 different blocks anywhere in the pyramid.

Update: Just to clarify, thanks to GO WITH OREO for mentioning that the beacon cannot be built underground, which is mostly true. It can be built underground, but only if the actual Beacon block has a clear path to the sky without any obstruction

Also ItsVip3rCouchYo made the point that the beacon pyramid cannot be hollow and all layers must be full

All credits to Thrax33

In new Tutorial in 4 minutes only ^^

In the Tutorial world there is a small beacon already built. It's missing the 9 by 9 and the 7 by 7 level. Collect Iron, Gold & Emeralds to make blocks (You will need a lot). You can mix them up it doesn't matter but you need to make a pyramid. 9 blocks by 9 blocks is the bottom base and then 7 by 7 then 5 by 5 and then 3 by 3 and the beacon goes on top. Check out the video below to see what it looks like and where it is (2:05)

To see how to get all the achievements in the new Title Update check out my Achievement Review/Walkthrough

To create a beacon you need 5 glass blocks 3 obsidian blocks and the wither star. You need to kill the wither to get the star. To create a full powered beacon you will need to build a pyramid structured like this 9×9, 7×7, 5×5, 3×3, Beacon. The pyramid must be made using iron, diamond, gold or emerald blocks. They can be made in any combination of blocks. To make a block of iron, gold, etc you will need 9 ingots to make 1 block

Also to confirm you only need to be near the beacon when it is completed. You don't have to be the one to finish the build.

A quick tip if you already have a fully powered beacon in your world, you can simply break the beacon and replace it back on the top.

So if you happen to have already built one, there is no need to kill another Wither and build a new beacon! You can get this achievement in seconds!

For those like me who only have access to the latest Tutorial World (Aquatic Update) :

Launch a new Tutorial World, then skip everything, march forward until you get to the place where you can see the "sea" way down below. Just under the rocks you're standing on is the beacon with a chest containing 1 Gold block and 1 Iron block, you can use the same trick described by Yui Shojei in his solution, press B when tutorial shows up, open the chest, grab the 2 blocks, back out, and repeat the process until you get enough blocks (just follow his solution if you want to know how to fully power a beacon). If you need a pickaxe, just grab the iron ingots in this same chest, back to the starting place of the village to get some wood, and craft an iron pickaxe. You can also climb and try mining the blocks of the giant pickaxe in the "village" to speed up the process.

This all still works as of Aquatic Update, October 2020.
Run a tutorial world, You should find the beacon near the sea as you run down and it's a little tedious but create the 9 by 9, above 7 by 7, above 5 by 5 and 3 by 3. You can grab diamond, gold, iron or emerald blocks and they don't need to be placed in any sort of order. Then knock one of the beacons off the item frame and place it on top, make sure there is a hole above the beacon, if not, make one! Another tip, grab the diamond blocks off the diamond pickaxe and the start and just run around the town picking them up. You can get a pickaxe from near the blacksmith. Also, if you grab the blocks out of the chest in the beacon room, leaving the area and for a few seconds and coming back resets the chest with blocks. Good luck, super tedious ! x