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