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