Successfully complete one of the following tasks to get a trophy:

Co-op Campaigner (Bronze): Complete any multiplayer level.
Medic! (Bronze): Purchase the Health Kit Upgrade.
Smackdown (Bronze): In single player story mode, melee one of each
type of alien.
Protectionist (Bronze): In single player story mode, purchase 5
Hardened Armor items from the Intex Vendor.
Deadly Combo (Bronze): Kill a stunned alien with a Frag Grenade.
Rocketman (Bronze): Kill a sentry gun with one rocket.
Pathfinder (Bronze): Complete a single player level with Waypoiny
Display turned off.
Old Soldier (Silver): Complete all single player levels 1-5.
War of Attrition (Silver): Kill 1000 aliens in single player.
Vital Statistics (Silver): Finish 'Primed' single player level
with 300000 or more overall score.
Praemonitus Praemunitus (Silver): Collect all logs throughout the
game.
Survivor (Silver): Stay alive for 8 minutes on any of the Survivor
mode single player levels.
Rapid Deployment (Silver): Complete 'Cargo' multiplayer level in
10 minutes or less.
Super-Sleuth (Silver): Find all 'secret' collectibles.
Deadly Assassin (Silver): Without taking damage kill 50 aliens in
single player.
Material World (Silver): Buy every upgrade.
Lazy (Silver): In a multiplayer game, reach the end of a level
without dying or firing a shot.
Sentry Duty (Silver): In single player, use a sentry gun to kill
20 aliens.