There are 13 Trophies that can be collected.

Bronze

A Lil Problem    
Kill Lil in 5 different ways    

A Laarg Problem    
Kill Laarg in 5 different ways    

Test Subjects    
Use sheep as test subjects in 6 levels    

Trippin    
Trip up Lil in 5 rooms    

Splatter Fest    
Kill minions in 12 different rooms    

Prison Escape    
Escape the Prison    

Quittin' Time    
Escape the Factory    

Out of the Dumps    
Escape the Dumps    

Rock It!    
Escape the Workshop

Silver

A Cautionary Tale    
Collect all the warning signs    

Starry Night    
Earn 3 stars in every level    

Death Comes For Ye    
Die in every level in Escape Plan

Gold

A Clean Escape    
In challenge mode, complete the entire game in less than 20 deaths combined for Lil and Laarg

http://www.ps3trophies.org/game/escape-plan/trophies/