Here is the full list of all 19 Space Toads Mayhem achievements.
Pick up a Gun Timeout
Pick up a Vicious Red Hole
Pick up Sparks of the Thunder Gods
Achieve max gunpower
Pick up a Mega Death Sun
Pick up an Insta Death
Pick up a Mystery Drop
Pick up Space Spikes
Perform a Power Dodge
Beat the game on normal
Beat the game on hard
Beat the game on psycho
Beat a level with at least 50% accuracy
Beat a level with at least 75% accuracy
Beat a level with at least 95% accuracy
Beat the game without losing a life
Beat the game without losing a life on hard
Beat the game without losing a life on psycho
Beat a level without taking any damage