Here is the full list of all 24 Omega Strike achievements.
Buy a Chicken Treat
Defeat Wrassler
Collect 100 coins
Buy a weapon upgrade
Collect 50 coins
Defeat Dozer
Collect 10 coins
Open a chest
Find a Life Cube
Open 10 chests
Open all chests in one game
Find 10 Life Cubes
Collect all Life Cubes in one game
Buy a Grand Feast
Defeat Commander Armstrong
Defeat Drillmaster 5000
Defeat the forest guardian
Defeat Overseer Brodus
Defeat Colonel Gurtz
Defeat Garbage Disposal Unit X13
Defeat the Sky Commander
Defeat the Garbage King
Defeat OmegaBot-2000
Defeat Doctor Omega