The Adversary is a Chapter II branch of the Princess. She is found by hesitating before slaying the Princess, but ultimately finishing the job.
There are two branches of the Princess that can be found from the Adversary; The Eye of the Needle, which is found by fighting the Adversary with the blade, but dying anyway, and the Fury, which is found by denying the Adversary a good fight. You can also bring the Adversary to the Shifting Mound by baiting her into following you and leaving the cabin.