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