General Tips
F.E.A.R. isn't all that complicated a game; after you learn how to shoot a guy in the head, that's pretty much all you need to know, really. That said, here are a few tips that you might find helpful.
Don't Forget to Lean
You have lean keys for a reason. By default, these are bound to Q and E, and will allow you to lean left and right, respectively. Leaning will enable you to shoot without exposing a large amount of your body to enemy fire, which will, in turn, let you shoot without taking a lot of damage. Enemies will still be able to hit you, but weapons with large sprays, such as the RPL Submachinegun, will see most of their shells either miss you or hit your cover. So don't forget to lean; your enemies certainly won’t.
Know Your Weapons
One thing that's not immediately obvious about the weapons in F.E.A.R. is that holding different weapons will affect your movement speed. An RPL or a shotgun will enable you to move more quickly, but holding up a Type-7 or a MOD-3 will cut your speed drastically.
Since you can carry three weapons at any given time, it's often worthwhile to switch over to your shotgun or something that lets you move quickly when you're travelling around, then switch to your heavy weapons when the situation dictates and you're not required to move around as much.
Psychokinetic Damage
This is something you'll undoubtedly find out for yourself, but keep in mind that, during all of the many hallucination / psychic invasion scenes that you sit through, the specters within can do actual damage to you if they hit you. They have to impact you to deal any damage, though, so if you shoot them before they manage to impact you, you should escape unharmed.
Ramping Up The Difficulty
One way to increase the challenge of a game of F.E.A.R. is to increase the difficulty, of course, but if you're looking for a good amount of challenge without a stable of incredibly hard-to-kill enemies, you might want to consider simply disabling the slow-mo effect by unbinding the key that goes along with it. Unlike other games with bullet-time effects, F.E.A.R. has no sequences that are outright unplayable without the slow-mo. It's a more difficult experience, to be sure, requiring much more deliberate movement, forcing you to stick behind cover during most firefights and pick your headshots where you can