Here is the full list of all 15 Burn, Clown, Burn! achievements.
Complete the 1-st level
Smash yourself into anything hard enough and die
Perform 100 mighty good somersaults
Perform 3 successful jumps in just 7 seconds
Survive 100 deadly jumps over the flames of hell
Let ghosts scare you 13 times
Collect all the golden stars
Collect all the silver stars
Collect all the bronze stars
Collect all the infernal stars
Disassemble yourself 100 times
100 deaths in flames of hell
1000 deaths in the fiery furnace of hell
Die the very special way
Spend 5 seconds up in the air