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