Here is the full list of all 23 The Shape of Things achievements.
Solve 100 unique shapes
Obtain your first gacha!
Solve one shape in less than 30 seconds
Obtain 5 gacha!
Change the mood to a rainy night
Change the mood to a sunset
Obtain 10 gacha
Complete 10 shapes from the same world in less than 10 minutes
Obtain 30 gacha
Change the mood to a snowy morning
Spend 5 minutes enjoying time in your room
Spend less than 10 seconds to solve one shape
Reset a shape 5 times
Complete your first shape
Complete 25 shapes
Complete 50 shapes
Complete 75 Shapes
Complete all shapes from the "Underwater-Reef, Seashore, Fishing Boat" gacha
Complete all shapes from "Flower Field", "Pond", "Camping" gacha
Complete all shapes from the "Market Street & Candy Shop" gacha
Complete all pieces from the "Magic Room & Old Ruins" gacha
Complete all pieces from the "Art Studio, Classroom" gacha
Complete all shapes from the "Arcade & Gamer Room" gacha