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