I thought this little exerpt was very interesting:
"The grim purpose that burned inside him was growing, demanding direction, seeking release. He looked further, to the East. He learned karate from an ascended master in the Paektu-San mountains of Korea--Savate from a convicted killer living as a beach bum on an island off Borneo. Six months in a japanese hermitage taught him the value of Judo and Ju-jitsu. From a chinese woman so old she should have been dead, he learned the secrets of the Tao, that nothing is fixed, everything is fluid, everthing is energy. He mastered a dozen disciplines, experimented with them and fused them into something that was uniquely his own. In Africa he learned how to read the environment for the signs man's passage leaves--how to find and follow a trail to which ordinary men were blind...The ninjas taught him their secrets--how to use the shadows, how to employ psychology to win the battle before it's even fought--the precautions to take when you make yourself a target--and how to use fear." - Shadow of the Bat #0
Flashback to his training as he's shown kicking down a tree (Batman Black and White)
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Learns kung-fu from old grand master Chu Chin Li deeming Bruce as his favorite student (Detective Comics #599)
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Tsunemoto (the most deadly martial arts assassin of the Yakuza) teaches him how to anticipate his opponents moves against various enemies plus the secret of spiritual healing techniques. Later on, Tsunemoto comments Bruce was his best student (Detective Comics #599)
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Receives training under Kirigi for a year, an old martial arts master that very few people in the world have had the privilege to study with. Kirigi comments that Bruce has a natural genius for mastering combat techniques due to the great violent nature inside him (Secret Origins of the World's Greatest Super Heroes)
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Training under Richard Dragon known as the world's best martial artist (Richard Dragon #7)
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Wildcat revealing to Huntress that he taught Batman to box (JLA #28)
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Learning the ways of Taoism from Shao-La mostly on how to keep a clear mind (Legends of the Dark Knight #52)
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Learning the secret arts of Taoism from H'sein-Tan (Legends of the Dark Knight #53)
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After his back is broken, he seeks out training from Lady Shiva to regain his physical prowlness and mastery of martial arts. Shiva is regarded by many as the world's deadliest martial arts assassin who Batman considers to be one the very few martial artists in the world that is his equal if not slightly better (Batman #509)
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We see Batman having a flashback of his training with David Cain as he's sparring with Cain's daughter Cassandra Cain (Batgirl) who's one of the best martial artist alive. David Cain taught Batman martial arts, weapon mastery, and fighting tactics. He's known by many as being one of the best assassins in the world also having invented a unique fighting style that involves the reading of body language. Here we see Batman defeat Cassandra in the sparring contest by using a modified deadly nerve strike (that was taught by Cain) to paralyze her. Being that violence is Cassandra's main form of communication (plus she was unable to talk at the time), it was the only way he could "speak" with her since she can read body language which enables her to anticipate attacks before her opponents make them (Detective Comics #734).
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