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