Easy completion of the game on Hard.
I'm not sure if this has already been posted but there is a really easy way to beat the game on hard so that you can get the achievement out of the way.
Like some of the games in the past (Bourne Conspiracy and Unreal Tournament III to name a few), you are not tied to finishing a level/mission/playthrough of a game on a specific difficulty from beginning to end.
You can switch the difficulty at the last checkpoint of a level/mission when you've played through it from the beginning up to that point on easy.
For F.E.A.R. 2, you can do pretty much the same thing.
In order to do so, get to the last checkpoint in each mission with enough grenades to kill yourself with. Once you do that, you get the options of loading the last checkpoint, quitting to the main menu and of course, change the difficulty.
I didn't figure this out till I finished the first 2 missions from beginning to end on hard. So I started doing this with the last checkpoint on mission 3.
I killed myself with the grenades, loaded the last checkpoint with the difficulty set to hard after playing most of it on easy, finished the mission, went to the main menu, went to mission select, looked at mission 3 and it said I completed it on hard. =D