Much like Durandal from Marathon we could see some sort of adversary in this newly rampant Cortana. This would explain the lack of depth on the details of rampancy; they want to delve into that in Halo 5. Cortana would make a great enemy as we would empathize with her, we would understand the struggle she is going though and, being one of the most loved characters in the series, we would want to save her while knowing that we had to stop her. Every strike against her would hurt us a players.

And what would make this fight even more interesting would be Cortana's perspective on the whole thing which we can see in her last line to the Didact:

Didact: Your compassion for mankind is misplaced.

Cortana: I'm not doing this for mankind!

She didn't sacrifice herself for the salvation of mankind. (In fact, she probably didn't like mankind much at all due to her rampancy) She did it for her love of the Chief. So that he could succeed and so that he could live on.
Much like Issac Asimov's artificial intelligence that was destined to manipulate the Three Laws of Robotics for the protection of humankind, every action of Cortana in Halo 5 could be to protect the Chief, even if it is at the cost of humanity.

So we have the Chief fighting to beat Cortana (and hating to harm her) and Cortana doing what she believes is best for the Chief. Motives of sacrifice abound.

This, of course, hinges on the idea that Cortana isn't actually killed off. I, for one, am kind of hoping for all of this.