Here is the full list of all 20 MatchyGotchy achievements. It takes around 8-10 hours to unlock all of the achievements on Windows.
Have your star fall asleep 10 times.
Take 300 selfies.
Win the game! Get 100% explored on Xanadu.
Play games a total of 50 times.
Build a total of 1000 ships.
Level Doctor UFO.
Clean up a total of 10 times.
Level Speedy Sputnik.
Level Loony Lander.
Level Guru Moon.
Let at least one star die.
Level Pirate Planet.
Level Spacey Galaxy.
Fill up hearts 100 times.
Eat 100 burgers.
Heal your stars a total of 10 times.
Experience sugar rush 10 times.
Build 10 ships and unlock Xanadu.
Survive all stages: smol egg, tiny baby, awkward teen, rocket surgeon.
Level Matchy Star.