Here is the full list of all 14 Rise of the Slime achievements.
Push a button
Set up camp, grill some snacks, get some health
Travel trough a portal
Check out what is inside those pots
Get your first pet
Change your crown to something more fancy...
Teleport during combat
Acquire a core mutation
Finish your first run
Start a new run with unspent 3000 GP
Play 10 cards in one turn
Perform an execution
Win cash from the lucky wheel
Enter your second loop of the game