Here is the full list of all 24 Omega Strike achievements.
Defeat Commander Armstrong
Defeat Wrassler
Collect 100 coins
Buy a weapon upgrade
Buy a Chicken Treat
Defeat Dozer
Collect 50 coins
Find a Life Cube
Open a chest
Collect 10 coins
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 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