Here is the full list of all 51 Ninja Gaiden Σ Plus trophies - there are 42 bronze, 5 silver, 3 gold and 1 platinum.
Completed Chapter 1.
Obtain a scarab.
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.
Get platinum coins in all Ninja Trials.
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
Get 50,000,000 Karma.
Obtain 50 coins in Ninja Trials
Clear Unrivaled Meeting, Nightmarish Phantasms, Abysmal Lair, and Secrets of Shooting
Clear all Ninja Tutorials and Path to the Ultimate Ninja.
Defeat 1000 enemies with the War Hammer (Hayabusa).
Defeat 1000 enemies with the Wooden Sword/Unlabored Flawlessness.
Defeat 1000 enemies with the Dabilahro.
Defeat 1000 enemies with the Kitetsu.
Defeat 1000 enemies with the Vigoorian Flail.
Obtain all scarabs.
Find all Team NINJA logos.
Defeat 1000 enemies with the Lunar Staff.
Use Ice Storm successfully 100 times.
Use Inazuma successfully 100 times.
Use Inferno successfully 100 times.
Hold 99,999 Yellow Essence.
Use Sorcery successfully 100 times.
Defeat 500 enemies with Rachel.
Defeat 1000 enemies with the Dual Katana.
Use the Guillotine Throw on 100 enemies.
Use the Izuna Drop on 100 enemies.
Kill every enemy in all Ambushes.
Use Fire Wheels successfully 100 times.
Defeat 1000 enemies with the Dragon Sword.
Finish all chapters of the game.
Get 10,000,000 Karma.
Completed Chapter 15.
Obtain 30 scarabs.
Kill every enemy in 6 Ambushes.
Defeat 100 enemies with projectile weapons.
Completed Chapter 10.
Use the strongest Ultimate Technique on 100 enemies.
Be a Hero 100 times.
Obtain 10 scarabs.
Completed Chapter 5.
Kill every enemy in an Ambush.