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