This is the same as the similarly named achievement from the original 360 version.
Here is the original solution from Hoffman.
As soon as you beat the Destroyer, this achievement unlocks if you are playing on Normal or higher. All difficulty achievements stack, so if you don't want a second or third playthrough, just play on Apocalyptic the first time.
The upside of playing through more than once is that you are able to keep your abyssal armor, which makes you take less damage, and absorbs some of the enemies' health every time you attack.