Condemned 2: Bloodshot

To make things clearer:

Once you finished the game on any difficulty settings, FPS mode will appear in the difficulty selection screen, directly below "Hard". Choose this and play through the whole thing to unlock this Achievement.

Note that FPS mode is its own difficulty and you can't mix it with Hard mode.

You unlock FPS mode once you complete the game, under any difficulty. This mode works great once you have the Gold Plated achievement, since you unlock the best bonuses. You (usually) begin each mission with a firearm of some type, with infinite ammunition. Your priority in FPS mode should be to kill enemies from as far away as possible, since you have firearms with unlimited ammo.

You can still use melee weapons, for times (like when you avoid the falling elevator in the hotel) when you need to. Enemies do greater damage than Easy difficulty, but not as much damage as hard difficulty. Since FPS is its own difficulty, you will also need to complete the game on hard if you're going for all of the achievements.

Another thing to note is that you also have inifinte tazer in FPS mode, once you get to the 4th level in the game (where the tazer unlocks). You can use the tazer to immediately stun enemies and just shoot them once to finish them (therefore, you don't have to go for headshots), and sometimes the tazer can be faster than whatever weapon you currently are wielding.

Always try to get a better firearm than what you're carrying, but you shouldn't have too much difficulty with this mode especially if you remember enemy locations in this game.

*Update* Some helpful advice from one of our community members, NoDroidsAllowed. Please check the comments section for info.