There are 12 Trophies that can be collected.

Bronze

Master Your Craft    
Use a special move    

Tactical    
Unlock all weapons & ability upgrades    

Chapter Brother    
Complete a mission in co-op mode    

Relic Bearer    
Find all the collectables    

Emperor’s Champion    
Earn a gold Aquila in every survival challenge    

Bloodbath    
Achieve a 'Bloodbath' Kill streak    

Exterminatus    
Kill 5000 enemies in total

Silver

Victory for the Chapter    
Defeat the Warboss!    

Devastator    
Complete a mission without using melee    

Honour in My Shield    
Complete a mission without dying    

For the Emperor!    
Get over 50 kills with each weapon type

Gold

Chapter Master    
Play through each mission with two different Space Marines

http://www.ps3trophies.org/game/warhammer-40000-kill-team/trophies/