There are 16 Trophies that can be collected.

Bronze

First Steps    
Beat a Supersonic Ghost

Early Days!    
Win a point in a multi-player battle

Silver

Speed King    
Earn at least Bronze in all the Speed Challenges    

Weapon Master    
Earn at least Bronze in all the Weapon Challenges    

Skill Chief    
Earn at least Bronze in all the Skill Challenges

I am the best!    
Win a multi-player battle

Gold

Elite Champion    
Earn at least Bronze in all the Elite Challenges    

Silver Arrow    
Earn at least Silver on all Challenges    

Supreme Being    
Earn Gold on all Challenges

No one can beat me!    
Win 10 multi-player battles    

I have no peers!    
Download and beat a rivals time    

World Tour    
Win a multi-player battle on every course    

Flawless Victory    
Win a multi-player battle by winning every point

Platinum

Platinum Trophy    
All other trophies have been collected

2 Secret

http://www.ps3trophies.org/game/wrecked-revenge-revisited/trophies/