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