There are 14 Trophies that can be collected.

Bronze

25% Gold Collectibles Found    
Collect 25% of all Gold Collectibles     

50% Gold Collectibles Found    
Collect 50% of all Gold Collectibles

Pack Rat    
Collect all upgrades     

Bowling    
Kill an enemy with an object shot with G-Lifter     

Kiss Me Deadly    
Kill a human enemy with another enemy's body     

Unfriendly Fire    
Kill a human enemy with deflected bullets     

Death from Above    
Kill an enemy by falling on him     

Electrifried    
Electrocute a human enemy     

Second Amendment    
Kill 100 enemies using the Rock Blaster     

Death on Delivery    
Kill 100 enemies using objects shot or dropped with G-Lifter

Game Completed    
Defeat Maximillian

Silver

100% Gold Collectibles Found    
Collect 100% of all Gold Collectibles

Say Hello to My Little Friend    
Kill 2 or more enemies with a single exploding mechanical enemy

Gold

Speed Run    
Complete the game in 3 hours or less

http://www.ps3trophies.org/game/rochard/trophies/