There are 19 Trophies that can be collected.

Bronze

MISSION ACCOMPLISHED    
Complete the Campaign on Casual difficulty

UNDER DURESS    
Interrogate the sniper    

4'S COMPANY    
Play through an entire chapter with 4 player co-op    

CHALLENGE JUNKIE    
Complete all Challenges    

UNTOUCHABLE    
Complete a mission on Hardcore without getting healed    

TIME IS MONEY    
Complete a challenge    

KILLING MACHINE    
Kill 50 enemies in a single combo   

PROFESSIONAL WRESTLER    
Perform all 4 fully upgraded grab moves    

KNOCK, KNOCK    
Blow the factory gates!    

GUN SAFARI    
Use each weapon in the game to kill an enemy

BALKAN PARTY    
Complete chapter 1    

DESERT STORM    
Complete chapter 2    

URBAN PACIFICATION    
Complete chapter 3    

BURMA BREAKOUT    
Complete chapter 4    

FLORENCE NIGHTINGALE    
Heal 50 times    

RAINING DOWN FIRE    
Take out the weapons train    

BLANKET PARTY    
Perform all grab moves, melee attacks and team signature kills

Silver

THE EXTRA MILE    
Complete the Campaign on Hardcore difficulty

HANDS-ON    
Kill 2000 enemies using melee attack or grabs

http://www.ps3trophies.org/game/the-expendables-2/trophies/