Dealing with the Joker directly seems to present at least two insurmountable obstacles, in that he can’t be reliably killed or confined by any means. Even if you were to march straight into the cell where he’s being (temporarily) held and place a gun right to his head, something would invariably happen to keep you from pulling the trigger. He’d have a hollow tooth filled with Joker venom and spit it at you, or he’d reveal that his henchmen had already kidnapped your relatives and would kill them all unless you helped him escape, or some such nonsense. If it came right down to it, Batman would burst in at the last second and prevent you from killing him, so that’s no good. For much the same reasons, the Joker is automatically immune to any attempts to permanently cripple, lobotomize, or mentally alter him in any way. Don’t look at me like that; I don’t make the rules.
Contrariwise, if you actually *did * manage to blow his brains out, all that would prove is that he was never the *real * Joker after all; instead, you’ve just murdered some nameless hired impersonator or psychologically manipulated dupe. And if somehow the universe were looking the other way for a second and you did actually manage to really, truly kill the Joker, it’d only last for about two days until Mr. Mxyzptlk or Etrigan the Demon or someone would decide they were bored, and resurrect him just for the hell of it. That’s just the way the world works. So any resolution to the Joker problem must incorporate a plan that does not require him to be permanently incarcerated or killed, because it just isn’t going to happen.
My solution? Robot parrots. Lots of them. Gotham City needs to invest in flocks of highly sophisticated, autonomous robot parrots to patrol the entire city and its environs. As we all know, the Joker emanates a unique odor of soggy playing card dye and hydrochloric acid, that these robot parrots will be programmed to detect and follow. So whenever the Joker goes, he’ll be surrounded by dozens upon dozens of robot parrots, behaving ostentatiously. This will provide a ready means of tracking him, of course; but more importantly, everyone around the Joker will be distracted by the parrots.
Since the Joker thrives on attention, this should prove intolerable. He’ll be trying to poison the city’s water supply, and when he looks up, his henchmen are all smiling and laughing at the antics of the parrots. When he arranges to break all the inmates out of Arkham and send them on a rampage through the city, the other villains will be asking him, “Hey, what’s up with the parrots all of a sudden? Are you teamed up with the Penguin now?” Soon all the criminals will be talking about the new Joker/Penguin team.
The news media will pick up on it, and suddenly there’ll be stories like, “Parrot Puzzler: Has Joker Turned Pirate?” People will see the Joker committing a crime, surrounded by parrots, and they’ll go, “Hey, look out, it’s the Pirate!” And the Joker will be like, “Shut up! Shut up! I’m not a stinkin’ pirate, so just shut up!” And the next day, the newspapers will all read, “Pirate Loots Again!” “Pirate/Penguin Crime Spree Continues!”
Sooner or later the Joker will start to hate the parrots even worse than Batman, and this will be his downfall, since robot parrots don’t really count as an archnemesis. Bereft of focus, he’ll eventually get sick of the whole thing and leave town. Maybe every so often he’ll read about one of Batman’s escapades and think about going back to a life of crime, but then he’d run across an article asking, “Whatever Happened to the Pirate?” and he’d remember those damn parrots and reject the notion in disgust.
Granted, maintaining thousands of robot parrots will be no small expense for Gotham City, but I think it’d be worth it to get rid of the Joker once and for all. And honestly, after decades of notoriety as the town where the Joker could escape at any moment and kill your ass, I expect Gotham would jump at the chance to be known as the city full of happy, colorful parrots. “Welcome to Gotham City, Parrot Paradise!” the postcards would read. And you know the Penguin would always be trying to subvert the parrots to his own nefarious ends, so that would give Batman something to do. So everyone’s happy.