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