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