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