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