Here is the full list of all 24 Omega Strike achievements.
Find 10 Life Cubes
Defeat the forest guardian
Open 10 chests
Defeat Drillmaster 5000
Defeat Commander Armstrong
Defeat Wrassler
Collect 100 coins
Buy a weapon upgrade
Defeat Dozer
Collect 50 coins
Find a Life Cube
Open a chest
Collect 10 coins
Open all chests in one game
Collect all Life Cubes in one game
Buy a Chicken Treat
Buy a Grand Feast
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