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