There are 36 Trophies that can be collected.

Bronze

Too Hot For You    
Kill Brutal Maul without being frozen by his shockwave.     

Brutal Kill    
Kill 5 enemies at the same time.

Famous Hunter    
Kill 1000 enemies in total.     

Faster Than You!    
Use Counterattack 100 times.     

Grasshopper    
Use Dash 30 times without touching the ground.     

Curious    
Find half the notes.

Ready To Fight    
Find all types of equipment.     

Unstoppable    
Win any Outbreak match.     

Out of My Way    
Kill an enemy player in an Outbreak match.

Experienced     
Play 5 Outbreak matches.     

I'm Rich    
Find all the chests in story mode on the Normal difficulty level.

Double Attack    
Kill 25 heavy enemies using the Time Rewind double attack.     

Angry    
Kill 100 enemies during your Time Rewind Berserk buff.     

Rain of Bullets    
Shoot off Magic Armor from 50 enemies using Time Rewind clones.

Silver

Annihilation Kill    
Kill 10 enemies at the same time.

Collector    
Find all the notes.

Outbreak Hero    
Kill each Outbreak boss at least once.

Treasure Hunter    
Find all the chests in story mode on the Hard difficulty level.

Platinum

Platinum    
Awarded for successfully collecting all trophies.

17 Secret

http://www.ps3trophies.org/game/blades-of-time/trophies/