As the Honest Trailer points out, they had the best Joker - yes, really, what of it? - in Mark Hamill, Kevin Conroy's voice acting and performance as Bruce Wayne / Batman was note-perfect, and it arrived at the perfect time in the cultural zeitgeist.
This part really is important, because that's the part that most people forget. When 'Batman: The Animated Series' arrived on our screens, this was long before the internet and long before the saturation of content of this kind. Keep in mind, 'Batman Forever' and Val Kilmer was the order of the day for the character.
Of course, it being Honest Trailers, there's also a dig or two about repetitive moments - like Batman fighting animals constantly, or maniacal laughing on a regular basis. Still, if that's what you're complaining about, you've got nothing to complain about.