Here is the full list of all 31 Jet Kave Adventure achievements.
Finish any level without defeating a single enemy
Kill 3 enemies with a single jetpack charge
Avoid crashing into the ground on level 1-2
Beat Flint the caveman without letting him jump on the wall
Finish level 1-5 without using the slingshot
Kill an enemy and open a flower with a single shot
Complete a Time Challenge despite eating on the level
Jetpack charge 10 times without touching the ground
Disregard the warning at the beach
Fall on the fish face down
Destroy 30 nutshells
Screenshot the birth of a friend
Taste all kinds of food
Find the secret workforce behind wooden platforms
Finish all chase sequences without getting a single hit
Destroy all pterodactyl nests
Cut off the second head from all allosauruses on level 4-4 but kill none of them
Fall from more than 100 meters
Return to Era's shop after you bought everything
Gather 9999 shells
Eat 3 times during the boss fight on level 4-4
Finish the following levels without collecting a single shell: 1-4, 3-2, 3-8, 4-1, and 4-6
Beat the No Damage Challenge on all levels
Beat the Time Challenge on all levels
Beat the Collectible Challenge on all levels
Detonate yourself
Restart any level less than 10 seconds in
Trigger an idle animation
Spin the same spinning sign 4 times
Complete the game in the Arcade Mode
Achieve all feats