There are 35 Trophies that can be collected.

Bronze

Seasoned Squaddie
Complete any multiplayer level.

Bigger is Better
Purchase any weapon upgrade.

Version 2.0
Purchase an item upgrade.

At Your Mercy
Kill a stunned alien with a Frag Grenade.

The Initiated
Complete the prologue on any difficulty level

Bigger Isn't Always Better?
Kill a sentry gun with the Blaster.

Networking
Complete any co-op assault map over PlayStation Network.

Exploding Fist
Kill 3 burster aliens with one melee attack.

Into the Kill Zone
Kill 20 aliens with one sentry gun.

Recon Unit
Complete any single player level with the waypoints turned off.

K.I.A.
Locate the bodies of Vance and Barnes.

Silver

Battle-hardened
Complete all single player levels 1-5.

Immobilised
Use a stun grenade to stun 10 aliens at the same time.

Frag-master
Use a Frag Grenade to kill 10 aliens at the same time.

The Informed
Collect all logs through out the game.

Survivor
Stay alive for 8 minutes or better on any of the Survivor mode single player levels.

Meat Grinder
Kill 250 aliens on any of the Survivor mode multi player levels.

Hidden Treasure
Find all 'secret' collectibles.

Tank
Take 200 damage without dying on 'Determination' single player mission.

Survivors
Achieve a time of 8 minutes or better on any multiplayer survivor map.

Light 'em up!
Kill 5 aliens with one shot of Project X.

Gold

Elite Unit
Complete all single player levels 1-5 on elite difficulty.

More Speed, Less Haste
Complete 'Vengeance' single player level on Veteran mode in 17 minutes or less.

Can't Get Enough
Complete the prologue, all single player, co-op assault and survivor maps.

Hardcore
Complete any single player level using only the Blaster and Grenades.

Platinum

The Completionist
Each and every trophy has been awarded. Congratulations!

9 Secret

Bronze

Hard Up?
Sell any item.

Sunny Side Up?
Kill an alien egg using the melee attack.

Shattered
Smash 10 windows.

Grave Robber
Collect 50 items or weapons from human corpses.

Lost?
Access the map screen.

Silver

Exterminator
Kill 1000 aliens in single player.

Idle Sentries
Finish any level with five Sentry guns in your inventory.

Systems Crash
Kill Mia.

Regicide
Destroy the alien queen.

http://www.ps3trophies.org/game/alien-breed-3-descent/trophies/