While drifting in and out of sleep after seeing the other villains I kept imagining one of the other heroes going "Gee, Sweetheart, how come you get to have TWO nemeses (Bitterbat and the clown dude)?" And Sweetheart being unable to give a straight answer
The Jollies wind up becoming ERRBODY'S nemesis that's a hero because they are that much of a problem that the city just puts out a "GET THEM ON SIGHT" for all the heroes.
Cackle does def prefer fighting Sweetheart though because she is the most skilled at what she's doing but on paper, Bitterbat's her only official archenemy.
That being said, Sweetheart, if faced with the teasing, would def respond with "I don't fuckin want the killer clown PLEASE SOMEBODY ELSE TAKE HIM I CAN'T DEAL WITH HIS ASS NO MO'"