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