The general storyline claims Bruce, after he became an adult, learned his techniques from Tibetan monks. They didn't directly teach him, but he learned through his time in a monastery. There is other variations aswell, such as him fighting in gladiators, or a particular monk training him in everything.
That mentioned, the most substantial problem is his reliance on his villains. Joker, for example, is closer to Batman than his own allies. It is a thin line between love and hate and Batman ignores the line. He needs Joker to make himself feel sane. There was even a comic (The Joker | Injustice: Gods Among Us) where Superman killed Joker because Batman wouldnt. Later in the Batcave, Superman gets into an argument with Batman, where he accuses Batman of missing the Joker, of missing the fights. Batman stays silent.
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