You can beat a toxic person at their own game by setting boundaries and establishing clear boundaries in regard to their actions that you will not and cannot put up with the things they do.
Limit your contact, don't take it personally, use strategic empathy and embrace self compassion as well as be assertive.
The more irrational and off-base someone is, the easier it should be for you to remove yourself from their traps.
Quit trying to beat them at their own game.