Here is the full list of all 31 Jet Kave Adventure achievements.
Return to Era's shop after you bought everything
Gather 9999 shells
Jetpack charge 10 times without touching the ground
Spin the same spinning sign 4 times
Restart any level less than 10 seconds in
Eat 3 times during the boss fight on level 4-4
Cut off the second head from all allosauruses on level 4-4 but kill none of them
Find the secret workforce behind wooden platforms
Kill an enemy and open a flower with a single shot
Taste all kinds of food
Destroy 30 nutshells
Destroy all pterodactyl nests
Disregard the warning at the beach
Screenshot the birth of a friend
Finish level 1-5 without using the slingshot
Kill 3 enemies with a single jetpack charge
Beat Flint the caveman without letting him jump on the wall
Avoid crashing into the ground on level 1-2
Finish any level without defeating a single enemy
Trigger an idle animation
Detonate yourself
Fall on the fish face down
Complete a Time Challenge despite eating on the level
Finish all chase sequences without getting a single hit
Fall from more than 100 meters
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
Complete the game in the Arcade Mode
Achieve all feats