Like others, I was having problems with this achievement. The Ender Egg is right in the middle untouched, and the 4 End Crystals are all in the correct spots. For whatever reason, maybe due to it not being supported because it's an old world, the Ender Dragon wouldn't spawn. But luckily, there's still a way to get the achievement without having to start a new world.
What you need to do is go into the options of your world, and select "reset The End", which will make the Ender Dragon spawn as normal. Once you've went into the End and killed the Dragon now you should be able to make it respawn by placing the 4 End Crystals on each side of the exit portal, across from each other. Should look like this:
So the positive is that you'll still be able to get the achievement. The negative is you have to fight the Ender Dragon again. Oh well, if you did it once you'll be able to do it again!