Unfortunately this achievement requires you mine alot of iron, I mean a whole lot. 1476 ingots to be exact. This is because you need 164 iron blocks, and since it takes 9 ingots to make a block, 9 x 164= 1476. I should mention this can also be done using either gold, diamond, or gem blocks, but since iron is signifcantly more common then these, it's your best bet. The reason you need so much is because there are 2 requirements to this achievment, 1 is to build a beacon, and the other is to fully power it. Building the beacon itslef can take quite a while, it requires 5 glass blocks, 3 obsidian, and a nether star, looking like this (G=glass block, O= obsidian, N= nether star)
G G G
G N G
O O O
Obviously the only difficult to obtain piece is the nether star, which can be only obtained by killing the wither, which is quite a task in itself and I won't go over here.
The beacon, when placed, sends a beam of light into the sky. When placed on normal ground thats about all it does, however, it can be powered to create a buff which gives all players close to it an ability, such as increased speed, jumping, strength or health.
There are 4 levels available to pwoering up the beacon, each on only increases the range of the previous. To power it up you must build a pyramid out of the iron blocks, with the beacon sitting on top, The lowest power is simple a 3 x 3 square, with the beacon placed in the center. By adding underneath it a 5 x 5 square it is level 2, followed by a 7 x 7 then finally a 9 x 9 square meaning it is fully powered. So to fully power it you must make a square pyramid out of iron blocks with a base of 9 x 9 blocks, and the beacon in the center. As soon as you place the beacon the achievement unlocks.
The trouble with this achievement is the amount of time it will take you to get such a crazy amount of iron. If you are not up to the task of getting such a stupid amount of iron, you can always use the duplication glitch, which requires you make only 1 iron block and have built a double chest, the other guides explain how to do this glitch. An even quicker method is by just going into the tutorial, as there is a beacon already built with the top two levels there, so you do not have to craft a beacon and duplicating the items happens much faster.