To unlock you must simply complete the story mode beating all eight opponents using Aria on any difficulty earning any objectives.
If you want progress towards :
She has three objectives, and all can be completed in one run.
1) Beat story mode. Simply win all eight fights.
2) Beat story mode on at least hard difficulty. Change the difficulty to hard, then beat all eight fights.
3) Ultra combo Omen. Simply beat Omen with an Ultra in the final fight. Her ultra is
when Omen's health is reading 'danger'.