There are 45 Trophies that can be collected.

Bronze

A Cry of Anger    
Activate Burst 50 times.     

A Roar of Fury    
Activate Burst 100 times.     

Hit'Em Hard    
Defeat 100 enemies with a special attack.     

Hit'Em Harder    
Defeat 300 enemies with a special attack.     

Can't Touch This    
Perform 50 counterattacks.     

Can't Touch That    
Perform 100 counterattacks.     

They Don't Stand a Chance    
Defeat 50 enemies while in Unlimited Mode.     

Unstoppable Force    
Defeat 100 enemies while in Unlimited Mode.     

Taking Out the Trash    
Defeat 300 enemies with heavy attacks and/or lock-on fire.     

Quick on the Draw    
Achieve 70 EXCELLENT synchronic impact rankings.     

Lightning Reflexes    
Achieve 150 EXCELLENT synchronic impact rankings.     

Be the Fist    
Achieve an overall synchronic rate average of 80% on any difficulty.     

Pain Is Universal    
Accumulate a total of 10000 in damage.     

Too Legit to Quit    
Continue the game after falling in battle.

View of the Valley    
Continue to stare at the hot spring attendant's assets.     

Like a Fish    
Consume more alcohol than you should.     

Sometimes I Feel Like…    
Find all the peeping Doji at the hot spring.     

Shut Up, Wyzen!    
Interrupt Wyzen's monologue.     

Shut Up, Kalrow!    
Interrupt Kalrow's monologue.     

Shut Up, Augus!    
Interrupt Augus' monologue.

Silver

Look Ma, No Eyes!    
Complete the game with the Blind Master gauge equipped.

Ka-ching!    
Accumulate a total of 120000 Battle points.

Gold

Who Needs Health?    
Complete the game with the Mortal gauge equipped.

22 Secret

http://www.ps3trophies.org/game/asuras-wrath/trophies/