Canonically, we don't really see Azula struggle much with her identity besides in the beach episode a little bit and obviously her sudden breakdown. Psychologically, it seems that Mai and Ty Lee turning on her were a final nail in the coffin as to her own delusions of her self-image which were further shaken by her out of nowhere promotion to fire lord and the stress that accompanied it. Before Mai and Ty Lee betrayed her, she was able to rationalize her own family issues and lack of close relationships through the guise of them being traitors to the fire nation and defying the strict and cruel honor codes associated with it. But when the two people that she thought were her true friends turned on her, she could no longer ignore the reality that no one likes/respects her and she only rules through family ties and fear.
With all that in mind, Azula is aware enough to somewhat acknowledge her insane personality and upbringing under Ozai, and given the circumstances of her breakdown (becoming fire lord, eclipse, trying to kill her own brother once and for all), I can see her at being redeemed in some form without it being hacky. Then again, I haven't read the comic at all so I'm going solely off the show.