Surprisingly, this part is better than the first, which is a little rare. As always there are a few glitches in the rush to end the episode. But Mark Hamill as the Joker livens things up as always - there's nothing really new here from his portrayal in the Batman animated series, but he keeps things moving as you can easily tell by comparing this to part 1, which tended to plod in the early parts.
Clancy Brown gets to grow a bit which now looks to be a continuing arc for the character running on through season 2 (where the character begins to tie in to the comic book continuity, i.e., "President Luthor.") Brown perfectly voices Lex's growing frustration, pain, and relief at his final cure. Not to minimize the contributions of the other actors; the voicework overall is excellent, although not everyone gets much to do here. The Joker kinda takes center stage here and overshadows everyone but Lex.
The hints of a Cheetah/Batman romance are interesting even if it's Batman putting on a show - it's rare we see the Batman try to (literally and romantically) seduce a female opponent and you'd think he'd do it a bit more often. This is a guy who uses all his wiles to take down the bad guys, so a fake romantic interest doesn't seem beyond the question.
As to the League, Batman is in control as always and he's the centerpiece of the episode. His final speech to the Joker makes this clear (and explains why he was so easily captured in part 1), and watching him play off the villains against each other is fun. Superman finally gets to kick some butt rather than be everyone's whipping boy, but it's also amusing to watch his own reputation used against him by Copperhead, who knows the Big Blue Boy Scout can't do much against him.
The other heroes get their moments as well although not as much. J'onn seems downright dumb sometimes, unfortunately, although it's more that the writers don't seem to know how to handle him without his overpowering everyone. Still, given how well the writers balanced out the large groups of characters here, they shouldn't be afraid to do it more often in the future. It's fun watching the entire League pound on a team of opponents, even if the logistics for the writers and animators are no doubt a nightmare.
Overall there are some slow spots here and a few logic gaps (why is almost everyone standing around watching Superman interrogate Copperhead?) but this episode neatly mixes pathos, comedy, and good ole action adventure and starts off what looks to be a major Lex Luthor story arc running through the show for at least another year.