There are 12 Trophies that can be collected.

Bronze

The Adventure Begins    
Clear SYLVANIA CASTLE ZONE, Act 1.    

Rolling Combo!    
Activate the Rolling Combo with Sonic and Tails.    

Metal Sonic Falls    
Defeat Metal Sonic in SKY FORTRESS ZONE, Act 1.    

A Golden Wave    
Defeat all bosses as Super Sonic.    

All Stages Cleared!    
Defeat the final foe and watch the ending.    

Tag Partner    
Upload a Multiplayer score or time.    

I Love Tails    
Play as Tails 50 times.    

Ring Collector    
Beat Special Stage 1 after collecting every Ring.

Silver

Endurance Race    
Clear all stages without returning to the World Map.    

All Chaos Emeralds Found!    
Collect all seven Chaos Emeralds.    

Proof of Speed    
Clear SYLVANIA CASTLE ZONE, Act 1 in one minute or less.

Gold

All Red Star Rings Found!    
Defeat the final foe after collecting every Red Star Ring.

http://www.ps3trophies.org/game/sonic-4-ep2/trophies/