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