There are 28 Trophies that can be collected.

Bronze

The Defender
For completing operation 1

No One Left Behind
For completing operation 2

Last Minute Hero
For completing operation 3

Ruthless
For completing operation 4

Survivor
For completing operation 5

The Crusher
For completing operation 6

Rookie
For finishing all levels on rookie difficulty

Veteran
For finishing all levels on veteran difficulty

Marine
For 500 kills in total

Marksman
For 50 headshots in total

Chain A
For chain of 5 kills

Demolition Enthusiast
100 destructible objects destroyed in total

Bronze Bullet
For 15000 fired bullets

Trigger Happy
For finishing any mission with accuracy 5% or lower

Silver

Exterminator
For 1000 kills in total

Sharpshooter
For 100 headshots in total

Chain B
For chain of 7 kills

Demolition Man
250 destructible objects destroyed in total

Silver Bullet
For 20000 fired bullets

Pinpoint Accurate
For finishing any mission with accuracy 50% or higher

Close Call
For finishing any mission with only one Health bar left

Gold

John R.
For 3000 kills in total

Headhunter
For 300 headshots in total

Chain C
For chain of 10 kills

Demolition Addict
500 destructible objects destroyed in total

Golden Bullet
For 25000 fired bullets

Without a Scratch
For finishing any mission without being hit (except shooting ranges and “Hawk Eyes – The Escort”)

Platinum

Platinum Trophy
For collecting all trophies

http://www.ps3trophies.com/forums/ps3-trophy-news/6720-heavy-fire-afghanistan-trophy-list.html