It's actually quite a mistake on how Batman was trained...
Bruce learned all the basic core fighting arts as he was growing up, largely taught to him by Alfred. Alfred also taught him the art of disguise and theatre as well as throwing your voice and changing your voice and field medicine. Alfred was a Special Forces Intelligence agent and a stage actor before coming to work for the Waynes. Bruce took many private lessons at home, Alfred keeping him on the path, maximizing his education and training along with the help of Leslie Thompson. Assuming Bruce was brilliant to start off with most of the stuff he needed to learn he would have been one of the few people to actually be able to access to it all before the internet and it's actually quite easy to learn a lot of stuff if done right because they all re-enforce each other and build up. This allows him to have beyond a college level understanding of most things at very young due to access, level of knowledge, and breadth of knowledge.
That pretty much handles all the basic and would have put him on the Masters/PhD level for most subjects and if not a lot of the breadth of knowledge would cover for it. Once he hit 18-ish he started taking college courses from all the top schools, enrolling under various pseudonyms, but never doing too well. This indicates he didn't put much effort into the actual work, but listened and learned and given he was able to create these pseudonyms he could easily forge credits from other colleges letting him get into advanced classes where need be.
After or during this period he only sought out 7 "masters" that taught him in various areas... martial arts, mysticism, detective work, explosives, etc. He might have also trained with lesser masters a bit but only to learn the completion of the art. Despite what people think a lot of martial arts is just the basics + some other stuff that doesn't take long if you understand the core. Bruce trained the core so he didn't need to keep on relearning from the beginning like a lot of people picture in their heads.
Now... is he the best in any field? A few probably, intellectual fields because he has access to advanced tech and he has a huge breadth of knowledge which allows him to draw connections which allows him to advance faster. As far as martial arts... nope.
Shiva, Black Canary, Cassandra Cain, Cheshire, King Snake, Silver Monkey? I think one of their names were, they're on the top 10 martial artists list and possibly Tim Drake are all better martial artists than him. He's not the best martial artists, because he doesn't care about fair fights, honor, etc. He cares about winning and stopping you from hurting yourself and others. However he can do that the most effective way is the way he'll do it. Tim Drake has had better training and more masters than any of the Bat family and that's why he might be one of the top martial artists, but he's much like Bruce in that he doesn't fight that way. He wins. He doesn't care to be the top martial artist.
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