This can only be completed after you complete the Warlords of New York campaign. Difficulty of the mission does not matter.
After completing the campaign, you will unlock "Directives" which are modifiers that affect gameplay.
To access these, view the map, and hit right on the d-pad. From here, you can change the difficulty of anything you do, as well as set up to 5 directives.
For the achievement, you only need to select one. The directives may change over time, but as of the writing of this guide, they are:
Ammo Hoarders: Reduced starting ammo & excess ammo is lost of reload. Enemies don't drop ammo & ammo is not shown on the mini-map.
Cool Skills: When one skill is activated the other is put on cooldown.
Fog of War Revisited: Mini Map and directional threat indicators are removed.
No Regen: Armor never regenerates after an encounter. It can be manually healed.
Special Ammo: Enemy bullets may be of special types. What type depends on the enemy faction.
I chose to activate "Cool Skills" and I re-played the main mission "The Tombs" on Story difficulty.