Here is the full list of all 37 King of the Hat achievements.
Play 200 multiplayer games
Play 100 multiplayer games
Unlock all levels of Fatcat's Office
Win 5-0 in a 1v1 in Last Hat Standing
Unlock all item blocks
Unlock all levels of Cloud City
Play 50 multiplayer games
Unlock all levels of Hat Factory
Unlock all levels of The Void
Unlock all levels of Shrines of Hat
Unlock all levels of Cole's Place
Play 20 multiplayer games
Unlock all levels of Kiara's Castle
Play at 150% game speed
Play at 50% game speed
Unlock all levels of Super Hat Con
Play 10 multiplayer games
Join a friend online
Unlock all levels of Hatlandian Hills
Play 5 multiplayer games
Beat Arcade Mode
Beat Arcade Mode on Hard
Beat Golf with Fatcat
Beat Golf with Kiara
Beat Golf with Birthday
Complete the Tutorial
Crush 11 hats in a row
Crush 8 hats in a row
Crush 5 hats in a row
Crush 3 hats in a row
Unlock all characters
Make $1,000,000 Money
Make $100,000 Money
Make $250,000 Money
Make $500,000 Money
Make $750,000 Money
Open the game