Also, part of the problem is that while Azula can (and sometimes has) beaten Zuko in direct combat, that's not the win condition of the loop? Beating Zuko isn't enough. Beating Katara isn't enough. Even beating Aang or Iroh might not be enough, if she ever gets to that point. If it comes to a fight at all, that's a fail condition for that Loop, seemingly.
Because the person that Azula needs to beat, really? Is herself. Until she can overcome the spiritual and mental chains that are forcing her into the behaviors that she has had ingrained into her, there can be no victory. The Final Boss of this Quest is almost certainly going to be Azula.
I've been thinking that for, maybe not the
last loop, but an important step of her character development to reach the last loop, is beating her dad in a fight.
At this point I think she has good odds if she's capable of pushing past her mental hangups. Though I admit that that's a big if. If nothing else, he definitely wouldn't expect her to know lightning redirection. (Ozai isn't quite on Palpatine's level of constantly using lightning that bites him in the ass, but he's probably alive mostly due to Zuko and Aang not actually wanting to kill him.)
A solid portion of her issues are directly tied to her relationship with her father, and her valuing his opinion of her. If she's at the point where she can outright go, "No, you're wrong,", then she has a solid chance of having had enough character development that she'll probably be able to break free of the loop.
And he'd probably have as little patience for her challenging him in public as he did for Zuko, meaning it might end in an Agni Kai. At that point, being able to prove to herself that he isn't some unassailable force (she knows that Aang beat him, but he's the Avatar so that's easy to internally justify to herself), and that she's better than him and doesn't have to live in his shadow, might just be exactly what she needs to be able to firmly step away from him in a moral sense.
Also, it'd be a big, cool, and emotionally painful fight, but, you know, mostly the character development thing.