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