There are 11 Trophies that can be collected.

Bronze

Heads Will Roll    
Destroy five robots in two seconds.    

Drier Spin Cycle    
Perform a 540 degree flip in a vehicle.    

Use Your Head    
Destroy a robot using a robot head.    

Big Ben    
Sound the bell ten times within ten seconds.    

Head Hunter    
Collect 20 robot heads.

Silver

Advanced Head Hunter    
Collect 75 robot heads.    

Rocket Man    
Propel your vehicle 150 metres into the air, using any means possible.    

Square Eyes    
Sit in front of a TV for five minutes.    

The One Gnome To Rule Them All    
The gnome must be cast back into the fiery chasm from whence it came.    

Five Second Rule    
Pick up twelve toasted sandwiches.

Gold

No Turning Back    
Complete every level without using the time slider.

http://www.ps3trophies.org/game/doc-clock/trophies/