A Petticoat Duel is pretty much the same as a regular duel, except that it is fought between women and the duel is considered over when first blood is drawn, not when someone dies. The most famous one was between Princess Pauline von Metternich and Countess Anastasia Kielmansegg. The fame of this duel, besides the elevated status of the women, is owed to the fact that they fought topless to avoid infection in case their clothing contaminated the wounds. It is not 
especially common to fight topless, but supposedly the women in question were so fierce that their overseeing physician, Baroness Lubinska, suggested it for safety. Apparently the development of sepsis from having bits of fabric trapped in sword wounds was a thing with duels and resulted in several deaths.
The dispute was supposedly over floral arrangements for the Vienna Musical Theatrical Exhibition. It doesn’t make much sense to me, but I guess if you have limited opportunities to contribute to the world, as was probably common for women in 1892, then you might get a little protective over where you have some control. Either way, the women fought their duel, but it is not known who the winner was. Princess Pauline delivered the first blood wound, but Countess Anastasia delivered the more serious wound. Pauline sliced up Anastasia’s nose and Anastasia stabbed Pauline in the arm. Apparently they made up after this, but there’s no documentation that I could find over how the flower situation was resolved. Both ladies went on to lead full lives afterwards, neither dying of sepsis so it seems that the topless concept worked here.
Thanks for stopping by!
-Erin