You've tried resolution, win-win, and diplomacy.  You've tried avoiding the conflict, and exiting the situation.  Nothing has worked.

The person you have conflict does not want resolution, and does not want the conflict to end.  They either enjoy subjecting you to the conflict, or want you to give them something you don't owe them just to stop the pressure.

There's no relationship left to protect.  You don't want a person like this in your life.

All that's left is the conflict - do you give in, knowing that you will be giving in again soon, because they will know that they can pressure you for more?  Do you endure this unpleasant conflict forever?

The problem is the conflict.  To end it, and ensure this person doesn't do this again, you must make the conflict so unpleasant for them that they will not do it again.  You must go at them in the nastiest ways that you can, and you must continue after they have asked for resolution or an end to conflict.

In other words, mirror them.  Be even worse than them.  And do it until they cannot bear it any longer.  This way, they will not start conflict with you again.