Here is the full list of all 38 Valkyrie Champions achievements.
Complete a Mission
Complete Final Mission
Defeat a Boss
Fail a Mission
Unlock 3rd Valkyrie
Unlock 4th Valkyrie
Unlock 1 Skill
Unlock 10 Skills for a single Valkyrie
Unlock All Skills for a single Valkyrie
Deal 5,000 Damage on a single mission
Deal 10,000 Damage on a single mission
Deal 100,000 Damage on a single mission
Deal 500,000 Damage on a single mission
Earn 1 Gold Medal on Hard Mode
Earn 8 Gold Medals on Hard Mode
Earn 16 Gold Medals on Hard Mode
Earn 24 Gold Medals on Hard Mode
Earn 32 Gold Medals on Hard Mode
Earn 40 Gold Medals on Hard Mode
Earn 48 Gold Medals on Hard Mode
Reach Valkyrie Level 25
Reach Valkyrie Level 50
Reach Valkyrie Level 75
Reach Valkyrie Level 100
Purchase First Pet
Purchase First Outfit
Purchase 9th Weapon for any Valkyrie
Purchase 9th Spell for any Valkyrie
Purchase 9th Relic
Purchase 4th Outfit for any Valkyrie
Purchase 9th Set of Wings
Purchase 9th Pet
Purchase 16th Weapon for any Valkyrie
Purchase 16th Spell for any Valkyrie
Purchase 16th Relic
Purchase 8th Outfit for any Valkyrie
Purchase 16th Set of Wings
Purchase 16th Pet