Tin_Man said:
The point is that by learning 100+ styles of combat, he is able to face and beat virtually anyone who raises a fist against him.
*Groan*
In Batman's fictional world, where there are secret special techniques limited to one martial art, which only have one workable defence restricted to students of that one art, that makes sense.
The thing is that, in reality, if you take strikers from a dozen different martial arts, the kicks and punches etc. that they throw in combat are going to be almost entirely identical. We only have two arms and two legs and seriously there are only so many ways to throw a punch or a kick. There might be slight differences, but the someone who practices Muay Thai is going to be able to respond to pretty much everything that someone who practices Karate or Taekwondo throws at him. Now, while he himself might not be throwing a spinning back kick, the idea is not alien to him and he should be able to defend against it: bottom line, he doesn't need to know how to do it to sidestep it (and for the record, the majority of the time I've seen that spinning back kick in practice, the opponent's best defence isn't to respond with something flashy, but to sidestep and throw a right cross... which any striking martial artist will know).
More from my direct experience, I can tell you that the vast majority of throws in Judo and Jiu-Jitsu are easily found in freestyle wrestling, and a good wrestler will already know how to respond to everything Judo or Jiu-Jitsu practitioners will use to take him down (I'm a slightly above mediocre wrestler here, no formal Judo or Jiu-Jitsu training, and nothing a couple Jiu-Jitsu and Judo instructors have done to me in sparring or in my presence have surprised me or seemed alien to me). Likewise, someone with good Brazilian Jiu-Jitsu is perfectly capable of responding to what any wrestler, Sambo, Judo, catch-as-catch-can, Aikido, or any other martial art practitioner is going to do on the ground. It's just useless to do even five different martial arts for grappling and takedowns, because when it comes right down to it they all amount to basically the same thing.
If Batman were to have studied 3 or 4 different styles, that makes some logical sense: you don't find good punching in Jiu-Jitsu, or good grappling in kickboxing. But 100 is useless because the amount of overlap is ridiculous and any sensible person wouldn't waste so much time and effort relearning the same things under different names.