One important detail, Play on PEACEFUL otherwise there will be a endless amounts on Enderman in The End.
To get to the End you will need:
-12 Ender Pearls
-12 Blaze rods
-1 Crafting table
Firstly make blaze powder using the blaze rod. Next combine the Ender Pearl and the Blaze powder together to make the Eye of Ender.
Once you've made 12 or more Eye's of Ender hit LT and follow where the Eye goes, it should eventually lead you to a spot where the Eye just flies towards the ground. Dig straight down until you reach whats know as a Stronghold, follow the maze of hallways until you reach the portal, now place each Eye in a holder then jump in. Once inside keep walking until you reach multiple pilliars, start stacking blocks to the top to destroy the crystals. Once all crystals are destroyed start attacking the dragon, i recommend using a Diamond sword and waiting till he stops in the center. When you've finally kill the dragon jump in the portal that is created upon his death and the achievement will unlock.
Or for a Much more simply method you can join a game that the dragon has previously been killed in so when you make your way to the End you want have to deal with him at all, Once again just jump in the portal and the achievement will unlock.
Note: As pointed out by JTman4556, you can make a world on the same seed as the world you've collected the Eye of Ender on in creative and find the portal so you know where to go on your actual world.