Here is the full list of all 51 [NINJA GAIDEN: Master Collection] NINJA GAIDEN Σ achievements.
Finish all chapters of the game on Master Ninja.
Finish all chapters of the game on Very Hard.
Use Fire Wheels successfully 100 times.
Hold 99,999 Yellow Essence.
Defeat 1000 enemies with the Dabilahro.
Finish all chapters of the game on Hard.
Defeat 1000 enemies with the Dual Katana.
Defeat 1000 enemies with the Vigoorian Flail.
Use Inferno successfully 100 times.
Use the Izuna Drop on 100 enemies.
Get 10,000,000 Karma.
Finish all chapters of the game.
Find all Team NINJA logos.
Use the strongest Ultimate Technique on 100 enemies.
Completed Chapter 15.
Kill every enemy in 6 Ambushes.
Obtain 30 scarabs.
Defeat 1000 enemies with the Dragon Sword.
Defeat 100 enemies with projectile weapons.
Completed Chapter 10.
Defeat 500 enemies with Rachel.
Obtain 10 scarabs.
Completed Chapter 5.
Kill every enemy in an Ambush.
Obtain a scarab.
Completed Chapter 1.
Defeat 1000 enemies with the War Hammer (Hayabusa).
Defeat 1000 enemies with the Kitetsu.
Defeat 1000 enemies with the Lunar Staff.
Defeat 1000 enemies with the Wooden Sword/Unlabored Flawlessness.
Use the Guillotine Throw on 100 enemies.
Use Ice Storm successfully 100 times.
Use Inazuma successfully 100 times.
Use Sorcery successfully 100 times.
Obtain all scarabs.
Kill every enemy in all Ambushes.
Get Master Ninja on all chapters.
Get Master Ninja on all chapters on Hard.
Get Master Ninja on all chapters on Very Hard.
Get Master on all chapters on Master Ninja.
Be a Hero 100 times.
Get 50,000,000 Karma.
Clear all Ninja Tutorials and Path to the Ultimate Ninja.
Clear the trials from Unrivaled Meeting to Secrets of Shooting.
Clear the trials from Secrets of Fighting to Captivating Goddesses.
Clear the trials from Desperation to Giants of the Underworld.
Clear Unearthed Challenge and Eternal Legend.
Obtain 50 coins in Ninja Trials.
Get coins in all Ninja Trials.
Get platinum coins in all Ninja Trials.
Obtained all achievements.