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