There are 12 Trophies that can be collected.

Bronze

Beautiful Assassin    
The dancing lady in Chinatown must not be defeated!    

Shinobi Has Fallen    
How was that dive into the waterfall?    

Shuriken Rain    
Use 300 Shuriken.    

Behold! Emblem of Blue!    
Appreciate the SEGA logo.    

The Traps of Neo Zeed    
Trigger 10 bombs.    

Miraculous Ninja Arts    
Use all four types of Ninjutsu in one game.    

Impenetrable Wall    
Guard 10 attacks with your cross-guard.    

Shuriken Starburst    
Demonstrate Joe Musashi's 8-way Shuriken Attack.    

Shinobi Watches    
Stand atop the brick pillar in 3-1. Ninja style!

Silver

A Clash With Evil    
Defeat the Round 1 boss without using the 8-way Shuriken Attack.

Brawn Over Ninjutsu    
Finish 6-1 without using any Ninjutsu.

Gold

For Naoko. For peace. Shinobi forever!    
Rescue Naoko without using a continue.

http://www.ps3trophies.org/game/revenge-of-shinobi/trophies/