I just won this achievement, so I'll make a list as best i can from memory, I did this all in one play through just to be safe.
Pistol - You begin the game with this.
Scar - You begin the game with this.
FY71 - Commonly dropped by enemies.
Shotgun - Commonly dropped by enemies.
Submachine gun - Dropped by enemies about midway through the game.
Precision Rifle - Dropped by enemy snipers, check lookout towers.
Missle Launcher - In the munitions room in the school before you save the first hostage (Level - Recovery.) You'll come across plenty after that.
Gauss rifle - Given to you after completing the side objectives in the level "Onslaught", also available in the level "Reckoning"
Minigun - Dropped by a Nanosuited enemies in the mines (Level - Awakening), before you defeat General Tong, also available in the level "Reckoning"
Alien Moac - Given to you by Prophet in the level "Paradise Lost"