Here is the full list of all 51 Ninja Gaiden Σ trophies - there are 42 bronze, 5 silver, 3 gold and 1 platinum.
Collect all trophies.
Be a Hero 100 times.
Get platinum coins in all Ninja Trials.
Clear Unearthed Challenge and Eternal Legend.
Get coins in all Ninja Trials.
Use Sorcery successfully 100 times.
Clear all Ninja Tutorials and Path to the Ultimate Ninja.
Clear the trials from Unrivaled Meeting to Secrets of Shooting.
Clear the trials from Secrets of Fighting to Captivating Goddesses.
Clear the trials from Desperation to Giants of the Underworld.
Obtain 50 coins in Ninja Trials.
Get Master on all chapters on Master Ninja.
Get Master Ninja on all chapters on Very Hard.
Get Master Ninja on all chapters.
Get Master Ninja on all chapters on Hard.
Finish all chapters of the game on Master Ninja.
Finish all chapters of the game on Very Hard.
Get 50,000,000 Karma.
Defeat 1000 enemies with the Kitetsu.
Defeat 500 enemies with Rachel.
Finish all chapters of the game on Hard.
Finish all chapters of the game.
Use Inazuma successfully 100 times.
Use Ice Storm successfully 100 times.
Use Inferno successfully 100 times.
Find all Team NINJA logos.
Obtain all scarabs.
Kill every enemy in all Ambushes.
Completed Chapter 15.
Defeat 1000 enemies with the Dabilahro.
Defeat 1000 enemies with the Dragon Sword.
Obtain 30 scarabs.
Use the Guillotine Throw on 100 enemies.
Defeat 1000 enemies with the Vigoorian Flail.
Defeat 1000 enemies with the Lunar Staff.
Hold 99,999 Yellow Essence.
Defeat 1000 enemies with the Wooden Sword/Unlabored Flawlessness.
Defeat 1000 enemies with the Dual Katana.
Defeat 1000 enemies with the War Hammer (Hayabusa).
Kill every enemy in 6 Ambushes.
Defeat 100 enemies with projectile weapons.
Get 10,000,000 Karma.
Completed Chapter 10.
Use the Izuna Drop on 100 enemies.
Use the strongest Ultimate Technique on 100 enemies.
Obtain 10 scarabs.
Use Fire Wheels successfully 100 times.
Completed Chapter 5.
Kill every enemy in an Ambush.
Obtain a scarab.
Completed Chapter 1.