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