Here is the full list of all 45 Omega One achievements.
Reached the level cap of 50
Killed a total of 50 boss ships
Killed a total of 25 boss ships
Killed a total of 10 boss ships
Reach Level 20
Unlocked Ship: Wasp
Killed a total of 5 boss ships
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Viewed the high-score table
Reach level 5
reach level 10
Unlocked Ship: Tonic
Unlocked Ship: Hornet
Unlocked Ship: Galactica
Unlock weapon: Spreader
Unlock weapon: Needler
Unlock weapon: Cannon
Unlock weapon: Plasma
Unlock weapon: Flak
Posted your first online score
Killed A total of 1000 Ship Enemies
Reach wave 20
Killed A total of 500 Ship Enemies
Reach wave 15
Killed A total of 250 Ship Enemies
Score 20000 points
Pickup a total of 100 power up drops
Killed your first boss
Played 1v1 for the first time
Won a 1v1
Killed A total of 100 Ship Enemies
Score 9000 points
Killed A total of 50 Ship Enemies
Unlocked Ship: Razor
Pickup a total of 10 power up drops
Reach level 2
Score 5000 points
Reach wave 10
Score 1000 points
Reach wave 5
Died for the 1st time
Pickup your first power drop
Started the game (for stats purposes)