You can do this on any difficulty, mush like the main game you are marked on your speed, kills, treasures and accuracy. Killing rats and spiders will reveal extra treasure collectibles, and aim carefully with your guns.
You can ignore most of the executioners as long as you kill at least four in the whole campaign. You can earn and S rank on any difficulty and while playing co-op. Decide which difficulty and if you want to play with a friend. The achievement will unlock once you see the mission summary screen.