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