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