you can get in a relationship with the manticore if you get addicted to her venom after talking to her a bunch(just keep taking the h scene as far as she allows and then go right back to her, around 10ish times)
Addition to what the other user said: if I remember correctly, you'll also need to win a few times against the Manticore while in vaginal sex stance, in order to get in a relationship with her.