Well, the most powerful weapon available to deal with the League is the League. Someone mentioned Tower of Babel; that shows you that some other guy just imitating Batman gave them a rough time.
So, here’s what I’d do. First, I would, in disguise or through a proxy, make friends with Aquaman. Then, I’d convince him that the League needs to be more down-to-Earth. Get him to pitch the idea of a team operating out of a less well-equipped headquarters. A warehouse, for instance. And it couldn’t be anywhere too far from the action; let’s say Detroit. The roster would have to be a bit younger (and consequently less experienced) too. Maybe Arthur would be interested in working with people like Vibe or Gypsy.
Then teleport the whole place to the middle of the sun and forget about it.
Alright, alright, serious answer: Actually, I might still start the same way. Start with subterfuge. Get to know certain members of the League. Meanwhile, start running a smear campaign that paints the League as tyrants. Convince as many League members as I can that the JLA is a bad idea. That they should disband. Ideally, they’d shut down on their own, but they probably wouldn’t be that easily deterred. As a backup, I’d start trying to convince the government to try to shut them down. Frankly, the more I think about it, the more I realize I’d probably try to take after Norman Osborn in Civil War. Maybe a little more proactive and without doing anything explicitly illegal, but definitely along those lines. The best plans are the ones where you don’t have to lift a finger.