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