Honestly pretty much all of supes villains have been turned either into JL lv threats or supergirls. Darkseid, brainiac, Lex Luthor, live wire
Doomsday isn't a recurring enough antagonist, nor is mongol. Matallo isn't main arch enemy material either.
So that just leaves........Mr Mxyzptlk?
Funnily enough, this is the exact plot of Whatever Happened to the Man of Tomorrow. Villains from the future say that today is the day Superman is killed by his greatest foe. It turns out that it was meant literally: Mxyzptlk is an omnipotent being. He is thegreatest foe, even if he isn't the most notable.
That was actually pretty awesome. Particularly his motive rant.
"The big problem with being immortal is filling your time. For example, I spent the first two thousand years of my existence doing absolutely nothing. I didn't move, I didn't even breathe. Eventually, simple inertia became tiresome, so I spent the next two thousand years being saintly and benign, only doing good deeds. When THAT novelty began to fade, I decided to try being mischievous. Now two thousand years later, I'm bored again. I need a change. Starting with your death, I shall spent the next two millenia being evil! After that, who knows? Perhaps I'll try being guilty for a while."
I particularly like the next line.
"Did you honestly believe a fifth-dimensional sorcerer would resemble a funny little man in a derby hat? Would you like to see how I really look?"
Indeed. I'm not normally a fan of "comic dialogue" where they usually end up trying too hard, but Mxyzptlk made it work in that story. Probably because he actually WAS powerful enough to get away with it, and he's clearly not trying to be cool. He's just got a total "know what? fuck you" tone going on. ---
A hero's role is one that cannot be forsaken, Caring for those with hearts that are breaking.