There are 12 Trophies that can be collected.

Bronze

Multiply and Conquer    
Reach 10 combo multiplier in Tackle Alley    

The Jester    
Showboat down the field for 30 yards in one wave in Tackle Alley    

Cleaning Up    
Collect 5 score patches in one wave in Tackle Alley

The Immortal    
Complete a single player Tackle Alley challenge without losing a life    

Headbanger    
Collide 2 defenders into each other    

Jack of all Trades    
In Tackle Alley use jump, barge and slide on all of the appropriate tacklers in a wave    

It Begins    
Complete a wave

Silver

Parting Waves    
Complete all single player Tackle Alley challenges    

Tackle Master    
Complete all single player Vengeance challenges    

Born Winner    
Complete all single player Supremacy challenges

Relentless    
Complete an entire single player Vengeance challenge without giving up a score

Gold

Pole Position    
Score highest on every wave of a single player Supremacy challenge

http://www.ps3trophies.org/game/backbreaker-vengeance/trophies/