Here is the full list of all 51 [NINJA GAIDEN: Master Collection] NINJA GAIDEN Σ achievements.
Finish all chapters of the game on Very Hard.
Get 50,000,000 Karma.
Defeat 1000 enemies with the Dual Katana.
Finish all chapters of the game on Hard.
Clear all Ninja Tutorials and Path to the Ultimate Ninja.
Hold 99,999 Yellow Essence.
Defeat 500 enemies with Rachel.
Defeat 1000 enemies with the Dragon Sword.
Finish all chapters of the game.
Defeat 1000 enemies with the Vigoorian Flail.
Find all Team NINJA logos.
Obtain all scarabs.
Kill every enemy in all Ambushes.
Defeat 1000 enemies with the Dabilahro.
Get 10,000,000 Karma.
Completed Chapter 15.
Use the strongest Ultimate Technique on 100 enemies.
Obtain 30 scarabs.
Kill every enemy in 6 Ambushes.
Completed Chapter 10.
Defeat 100 enemies with projectile weapons.
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 Izuna Drop on 100 enemies.
Use the Guillotine Throw on 100 enemies.
Use Fire Wheels successfully 100 times.
Use Inferno successfully 100 times.
Use Ice Storm successfully 100 times.
Use Inazuma successfully 100 times.
Use Sorcery successfully 100 times.
Finish all chapters of the game on Master Ninja.
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.
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.