There are 12 Trophies that can be collected.

BRONZE

Hello World
Clear stage 1 on either side in story mode.

Chao!
Name your Chao for the first time.

Chao Raiser
Raise all 5 properties of any one Chao up to level 10.

HERO!
Clear HERO side in story mode.

DARK!
Clear DARK side in story mode.

Boss Attack
Clear all 3 modes in Boss Attack Mode.

Mission Complete
Win all A RANKs (5 A RANKs) in any one stage in story mode.

SILVER

Heaven or Hell
Raise a HERO Chao and a DARK Chao with your hero and dark characters respectively.

Beyond Good And Evil
Clear LAST part in story mode.

Speedy Racer
Win NO.1 in expert level in kart race.

Emblem Collector
Unlock 90 emblems.

GOLD

You Are The Legend
Win A RANK in all stages in story mode.

http://www.ps3trophies.com/forums/playstation-trophy-news/23228-sonic-adventure-2-trophy-list.html