Here is the full list of all 23 Bye-Bye, Wacky Planet achievements.
Perform a dash 100 times
Defeat a Super Computer
Buy all heavy weapons
Liberate island from the wild creatures
Buy all light weapons
Kill 500 bugs
Save Alan
Kill a researcher in aircraft (for Eve)
Defeat Giant Drone Boss
Start a rocket
Kill a researcher in aircraft
Find a tank
Kill 500 scientists
Get out of a lab
Find a train
Defeat M-bot
Buy all abilities
Complete the drone mission
Complete level 09
Perform a double jump 100 times
Die first time
Break 10 security cameras
Kill first enemy