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