Here is the full list of all 26 Ares Omega achievements.
You have reached character level 50!
You have reached character level 40!
You have defeated 150 Oppressors.
You have defeated Ares Omega.
You have fired 10,000 bullets.
You have defeated Deimos.
You have reached character level 30!
You have used 100 medkits.
You have defeated Phobos.
You have defeated 100 Harassers.
You have defeated Enyo.
You have defeated 75 Incinerators.
You have found 100,000 credits.
You have reached character level 20!
You have defeated the Exterminators on Floor 6.
You have defeated the Dominators on Floor 5.
You have defeated the Brawlers on Floor 4.
You have defeated 50 Prowlers.
You have reached character level 10!
You have defeated the Marauders on Floor 3.
You have defeated the Berserkers on Floor 2.
You have defeated the Reavers on Floor 1.
You have leveled up for the first time!
You have completed the tutorial.
You have defeated 200 Warriors.
You have defeated Ares Omega on PLUS ULTRA mode!