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