Here is the full list of all 31 Frogun achievements.
Beat Prickly
Win a race
Finish a level with the obsidian skull
Fall on water
Finish a level with both eyemeralds
Get all coins in a level
Finish a level without dying
Finish a level having found the notes
Beat Kicky
Beat Wintry
Beat Scorchy
Beat Hexy
Beat Beelzebub
Win all races
Finish a level under the time limit
Finish a level with all of the emblem pieces
Get all of the complete emblems
Buy a hat
Buy all hats
Buy all gallery images
Complete the bestiary
Get all health upgrades
Beat the Boss Rush
Beat the Brutal Rush
Take a photo of the scenery
Pose for the camera
Get a Max. Health Up
Own the Kiwi and Melon hats
Defeat a boss cosplaying as them
Finish a level without damaging any enemy
Hit Jake with something during a race