There are 51 Trophies that can be collected.

Bronze

Falcon Dive    
Learn the Falcon Dive.    

Sliding    
Learn how to slide.    

Kunai Climb    
Learn the Kunai Climb.    

Wall Run    
Learn the Wall Run.    

Flying Bird Flip    
Learn the Flying Bird Flip.    

Rope Crossing    
Learn how to cross a rope.    

Izuna Drop    
Learn the Izuna Drop.    

Ultimate Technique    
Learn the Ultimate Technique.    

Steel on Bone    
Cut down 100 enemies with Steel on Bone attacks.    

I Got Your Back    
Play a Co-op Ninja Trial with a partner.    

Initiation    
Play a Clan Battle.    

Teamwork    
Win 10 team battles.    

One Against the World    
Win a battle royale match.    

Shady    
Perform a betrayal.    

Sneaky    
Perform a ghost kill.    

An Honorable Death    
Perform harakiri.    

Snowman    
Play the Snowfield stage 10 times.    

Guardian of the Village    
Play the Hidden Village stage 10 times.    

Observer    
Play the Watchtower stage 10 times.    

The Spice of Life    
Get 10 customization parts.

Silver

Walking Dictionary    
Get 100 kanji.

29 Secret

http://www.ps3trophies.org/game/ninja-gaiden-3/trophies/