Je ne peux pas jouer les mégères qui ne trouvent pas de rival à leur hauteur !
If you strictly abide by grammatical number agreement, "leur" should be chosen. But the use of "leur" jumps out at me.
After all, the plural noun "mégères" does not refer to actual multiple people, but rather it is more about the same single person playing the role of several different "mégères", each ever so slightly nuanced, if you will.
So the temptation is great to use the singular "sa", the more logic-driven alternative:
Je ne peux pas jouer les mégères qui ne trouvent pas de rival à sa hauteur !
The only snag is that "sa" cannot help but jar with the plural "mégères", so I'm now tempted to change "mégères" into the singular:
Je ne peux pas jouer la mégère qui ne trouve pas de rival à sa hauteur !
The issue of the plural-singular mismatch has now been resolved, but herein lies another problem: In the idiomatic expression "jouer les + plural noun", I'm not sure if it is acceptable to use the singular form.
All in all, which is the most idiomatic way to express this idea?