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