Here is the full list of all 49 VALKYRIE ELYSIUM achievements.
Completed the tutorial
Purified a monster
Defeated two monsters with a single Lightning Bolt
Completed Chapter 1
Completed Chapter 2
Completed Chapter 3
Completed Chapter 4
Completed Chapter 5
Completed Chapter 6
Completed Chapter 7
Completed Chapter 8
Completed Chapter 9
Defeated Odin
Defeated Fenrir
Agreed to Armand's offer
Completed every ending
Completed a subquest
Completed 10 subquests
Completed 20 subquests
Completed all subquests
Obtained
Purified a Naglfar
Raised the Combo Gauge to 300 Hits
Purified a monster by pushing them into a hole or off a cliff
Landed a Soul Burst Level 3 attack
Landed a Soul Steal in midair
Landed a Nibelung Valesti I attack
Obtained a Hollow Blossom
Obtained every Hollow Blossom
Obtained a Verdant Blossom
Obtained every Verdant Blossom
Obtained a rune
Obtained every rune
Obtained every weapon
Upgraded every weapon to its full potential
Reached SSS proficiency with every weapon
Learned every Divine Art
Learned all of Valkyrie's skills
Learned every Einherjar attack and their normal attacks
Unlocked all terms
Unlocked an Einherjar memory
Unlocked all Einherjar memories
Completed the game on Normal difficulty
Completed the game on Hard difficulty
Unlocked every achievement
Completed Hilde's Vengeance
Completed Seraphic Gate
Completed the game on Valkyrie difficulty