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