What would've made it much better
Honestly, I always hated the lame "DNA patch" gimmick, because it made no sense. How would it transform Tim Drake into an exact genetic duplicate of Joker? To this day I still don't get if it was supposed to be the actual Mr. J embedded in the chip who jumped out and possessed Drake, or just a facsimile of all his personality traits meaning the real one never shows up at all in the future.
What would've fixed it I always felt was if it actually was just Drake driven mad dressing up like the Joker. For whatever warped reasons or personal demons he suffered from. That's such a more Batman-ish idea anyway; his greatest ally becomes his greatest enemy because of a deep personal trauma he suffered that Batman was responsible for. It fits so much more into the mold in which all the classic villains are driven by their psychoses in TAS, the microchip gimmick is more of a Marvel idea. It would've improved the climax immensely to have Drake be aware he is the Joker and doing it on purpose with his full knowledge and faculties, ranting to Terry and Bruce how they didn't understand, "You didn't stop me from becoming Joker Jr... now I did the only thing I could, I AM the Joker, and I'm finally going to defeat Batman!" It would've increased the pathos immensely and given us Batman's greatest, most tragic fight of his life. As it was it just kind of ends with an anticlimactic thud, with Terry taunting him and making Spidey-like jokes.
That leads to the other thing; Drake/Joker absolutely, positively should have died in the climax. It would've rounded out the story and completed the message: tragedy only ends in more tragedy, violence begets violence, mistakes of the past that go unanswered come back to haunt us, etc. Sure Bruce would've been wracked with guilt, but I'm not talking any more so or any more gruesome than the resolution of the Talia & Ra's episode, Joker/Drake had to die in the same way to complete the circle of the story and give the other characters a more somber, haunting lesson to learn from. To this day I still cringe at Barbara's lame last line, "You were just along for the ride Tim!" Well hooray, we're now in G-rated happily ever after territory here, I say BS. Have Drake be responsible for his actions and die a powerful death, that's so much more the spirit of what Batman is. Born in tragedy, end in tragedy, that sort of thing.