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