Here is the full list of all 23 The Shape of Things achievements.
Change the mood to a snowy morning
Change the mood to a sunset
Spend 5 minutes enjoying time in your room
Change the mood to a rainy night
Solve 100 unique shapes
Obtain 10 gacha
Complete 75 Shapes
Complete all shapes from the "Arcade & Gamer Room" gacha
Complete 50 shapes
Obtain 5 gacha!
Complete 25 shapes
Complete 10 shapes from the same world in less than 10 minutes
Solve one shape in less than 30 seconds
Complete your first shape
Obtain your first gacha!
Obtain 30 gacha
Spend less than 10 seconds to solve one shape
Reset a shape 5 times
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