Here is the full list of all 21 Beautiful Mystic Defenders achievements.
Purchased all upgrades.
Defeated monster king Moldark.
Achieved 90 gold stars in total.
Achieved 90 silver stars in total.
Defeated monster commander Grimm.
Achieved 90 bronze stars in total.
Achieved 60 gold stars in total.
Defeated monster commander Grimsbane.
Achieved 60 silver stars in total.
Achieved 60 bronze stars in total.
Defeated monster commander Venomghoul.
Achieved 30 gold stars in total.
Achieved 30 silver stars in total.
Level up Airi to 5.
Defeated monster commander Gnash.
Level up Sumi to 5.
Achieved 30 bronze stars in total.
Level up Yasako to 5.
In love with Takami.
Level up Kitsune to 5.
Defeated monster commander Blightwing.