Successfully complete one of the following tasks to get a trophy:

Learned the Reverse Wind (Bronze): Successfully perform the Reverse Wind technique.
Learned the Furious Wind (Bronze): Successfully perform the Furious Wind technique.
Learned the Shadowless Footsteps (Bronze): Successfully perform the Shadowless Footsteps technique.
Learned the Flying Swallow (Bronze): Successfully perform the Flying Swallow technique.
Learned the Flying Bird Flip (Bronze): Successfully perform the Flying Bird Flip technique.
Learned the Obliteration Technique (Bronze): Successfully perform the Obliteration Technique.
Learned the Ultimate Technique (Bronze): Successfully perform the Ultimate Technique.
Learned the Ultimate Guidance (Bronze): Successfully perform the Ultimate Guidance technique
Learned to the Counter Attack (Bronze): Successfully perform the Counter Attack technique.
Learned the Unrivaled Soaring (Bronze): Successfully perform the Unrivaled Soaring technique.
Learned the Invisible Path (Bronze): Successfully perform the Invisible Path technique.
Learned the Izuna Drop (Bronze): Successfully perform the Izuna Drop technique.
Learned the Guillotine Throw (Bronze): Successfully perform the Guillotine Throw technique.
Learned the Art of the Inferno (Bronze): Successfully perform the Art of the Inferno Ninpo.
Learned the Art of the Wind Blades (Bronze): Successfully perform the Art of the Wind Blades Ninpo.
Learned the Art of the Flame Phoenix (Bronze): Successfully perform the Art of the Flame Phoenix Ninpo.
Learned the Art of the Piercing Void (Bronze): Successfully perform the Art of the Piercing Void Ninpo.
Feat of a Hundred Slashes (Bronze): Achieve a 100-hit combo with any weapon.
Feat of a Thousand Obliterations (Bronze): Defeat 1000 enemies unsing Obliteration Techniques.
Feat of Ultimate Destruction (Bronze): Defeat 1000 enemies using Ultimate Techniques.
Izuna Drop Master (Bronze): Successfully use the Izuna Drop on 1000 enemies.
Guillotine Throw Master (Bronze): Successfully use the Guillotine Throw on 1000 enemies.
Dragon Sword Master (Bronze): Defeat 1000 enemies with the Dragon Sword.
Lunar Staff Master (Bronze): Defeat 1000 enemies with the Lunar Staff.
Falcon's Talons Master (Bronze): Defeat 1000 enemies with the Falcon's Talons.
Dual Katana (Bronze): Defeat 1000 enemies with the Dual Katana.
Kusari-gama master (Bronze): Defeat 1000 enemies with the Kusari-gama.
Eclipse Scythe Master (Bronze): Defeat 1000 enemies with the Eclipse Scythe.
Tonfa Master (Bronze): Defeat 1000 enemies with the Tonfa.
Vigoorian Flail Master (Bronze): Defeat 1000 enemies with the Vigoorian Flail.
Enma's Fang Master (Bronze): Defeat 1000 enemies with the Enma's Fang.
Ultimate Ninpo Master (Bronze): Chant 100 Ultimate Ninpo spells.
Rescued 100 ninja (Bronze): Rescue 100 people in need.
All missions successfully completed (Gold): Successfully complete all missions.
Master of the Secret Arts (Platinum): Obtain all trophies.

Additionally, there are sixteen secret trophies:

Completed Chapter 1 (Bronze): Successfully complete Chapter 1.
Completed Chapter 4 (Bronze): Successfully completed Chapter 4.
Completed Chapter 7 (Bronze): Successfully complete Chapter 7.
Completed Chapter 10 (Bronze): Successfully completed Chapter 10.
Completed Chapter 13 (Bronze): Successfully complete Chapter 13.
Cleared the Path Of The Acolyte (Silver): Clear the game on the Path Of The Acolyte.
Cleared the Path Of The Warrior (Silver): Clear the game on the Path Of The Warrior.
Ayane mastered (Silver): Defeat 1000 enemies in Ayane.
Rachel mastered (Silver): Defeat 1000 enemies in Rachel.
Momiji mastered (Silver): Defeat 1000 enemies in Momiji.
Mastered the Path Of The Acolyte (Silver): Master the Path Of The Acolyte.
Clear the Path Of The Mentor (Silver): Clear the game on the Path Of The Mentor.
Clear the Path Of The Master Ninja (Silver): Clear the game on the Path Of The Master Ninja.
Mastered the Path Of The Warrior (Silver): Master the Path Of The Warrior.
Mastered the Path Of The Mentor (Silver): Master the Path Of The Mentor.
Mastered the Path Of The Master Ninja (Gold): Master the Path Of The Master Ninja.