Just as Halsey finds a cure for Cortana, she goes mad, and flees to a Forerunner device, and takes over the Prometheans.
Chief tries to stop her, and gets badly punched on the way; Didact goes full offense on her, and his ex-minions, but Cortana takes over his suit, and strips him off of it.
Cortana goes mad, and flees to Earth with the Promethean army and the Covies, who think she is the Didact.. Chief and Didact go on a truce to stop a bigger enemy: Cortana.
On a side-story, Didact and Cortana learn the Librarian might be alive, both go on a hunt for her.