There are 12 Trophies that can be collected.

Bronze

88 Miles per Hour    
Travel through time     

Just one hug is enough    
Get a hug from Amy     

Paradise Found    
Complete a zone in the Good Future     

Take the High Road    
Pass the upper Signpost in Collision Chaos Zone 2

Statue Saviour    
Find the angel statue in Wacky Workbench     

Heavy Metal    
Defeat Metal Sonic without getting hurt

Dr. Eggman Got Served    
Destroy Dr. Eggman's final machine

Silver

King of the Rings    
Collect 200 Rings

All Stages Clear!    
Finish the game

Just in Time!    
Complete the Time Attack mode in under 25 minutes     

Saviour of the Planet    
Destroy all the robot teleporters and Metal Sonic holograms in the past

Gold

Treasure Hunter    
Collect all the Time Stones

http://www.ps3trophies.org/game/sonic-cd/trophies/