All of the "Complete Act -" achievements come with the completion of the act mentioned in the achievement. "Assassin" and "Easy" difficulties are stackable, but Killer isn't as it needs to be unlocked. Unless you're completely new to shooters, you might as well save yourself some time and start on Assassin as it's really not difficult at all. You can't miss any of these if you complete the entire story, unless you have cheats enabled, of course. If you're having trouble with the Killer difficulty, make sure you're sticking to cover and use your bullet curves as much as you can. Take as much time as you need (or can) to make sure your shot is lined up.