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