Here is the full list of all 22 Tower of Waifus achievements.
Clear the 2nd floor
Defeat enemy with at least 16 Moves remaining
Play a training battle
Clear the 1st floor
Clear the 3rd floor
Clear the 4th floor
Clear the 5h floor
Clear the 6th floor
Clear the 7th floor
Clear the 8th floor
Clear the 9th floor
Clear the 10th floor
Deals 250 or more damage in a single move
Active spells 50 times
Starting the battle with a bonus Moves
Accumulate 30 Mana in one date
Create a super gem by 7 adjacent gems matched
Max all stats
Owned at least more than 20 spells at the same time
Starting the battle with a bonus Rage
Starting the battle with a bonus Mana
Starting the battle with a bonus HP