There are 12 Trophies that can be collected.

Bronze

Appetizer    
Win your first race (Single player)

I can’t stop!    
Collect 100 boost tokens

Goon riding, hah!    
Perform 100 Stunts    

Runway runaway    
Land in the target zone 50 times    

Power Extreme!    
Activate Recharge 66 times    

Detour    
Activate a Shortcut 50 times

Feel the connection    
Win a multiplayer race

Silver

The day I won it all    
Win all races in all tournament cards including Offroad Elite races

Mad skillz, I has them    
Perform 250 Stunts

Racing nobility    
Win all "Offroad Elite" events

Here for the long ride    
Achieve level 10 in multiplayer

Gold

Done and done    
Win the last Tournament race (complete the tournament)

http://www.ps3trophies.org/game/mad-riders/trophies/