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