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