There are 12 Trophies that can be collected.

Bronze

Pipe Wielder
Wield the Pipe in single-player or co-op mode.

Knife Wielder
Wield the knife in single player or co-op mode.

Psycho
Kill 10 enemies without losing your weapon.

Perfect Boss
Beat the first boss without dying.

First Versus
Beat another player in an online versus match.

Online Co-op
Complete an online co-op game.

Kill Jet
Defeat Boss 'Jet" at the end of Stage 2 -- With Game Settings set to Hardcore.

Silver

Fourth Boss
Beat the fourth boss.

Online Warrior
Beat 10 opponents in online versus mode

High Score
Score 800,000 points in one game -- with Game Settings set to Hardcore.

Hard Win
beat the game without special attack.

Gold

Perfect Win
Beat the game without continuing.

http://www.ps3trophies.com/forums/trophy-news/61959-streets-rage-2-trophy-list.html