This is the same as the similarly named achievement from the original 360 version.
Here is the original solution from m0rph3us17.
Fairly straightforward, this requires you to beat the game on Apocalyptic difficulty.
The main difference between this and Normal difficulty is that hits inflict a lot more damage. Enemies (including bosses) still seem to have roughly the same amount of health from what I observed. However, if you've already played the game a bit and are used to the combat (particularly dashing, knowing what weapon to use when, and knowing when to block/counter), this helps a lot.
You will also find this easier if you acquire wrath cores and lifestones as early as possible in the game.
Note that if you have won the Abyssal Armour on a previous playthrough, you will be given the option of carrying this over when starting a new game (this is the only item that you have the opportunity to carry over). If you choose to do this, Apocalyptic difficulty is actually not much tougher than Normal - the Abyssal Armour substantially reduces damage taken and also leeches health from enemies when you damage them.