"He has studied Biology, Technology, Mathematics, Physics, Mythology, Geography, & History. Gained degrees in Criminal Science, Forensics, Computer Science, Chemistry and Engineering by the time he was 21. He has mastered Diverse Environmental Training, Security Systems, and illusion/sleight of hand by the time he was 23. He gained even more degrees in Biology, Physics, Advanced Chemistry, and Technology by the time he was 25. He has learned Forensic, Medical Sciences, Expanded Computer and Engineering Sciences, and Expanded Device Pool use of personal powered armor and system, database creation on underworld crime bosses, rogue's gallery foes and other supers; improved material sciences for body armor and micro-machinery by the time he was 26. Has also learned Advanced New Development in Forensic and Medical Sciences."
Taken from batman.wikia.com
It's really specific so it makes me think that it's true but I can't find scans for it anywhere. It's much easier to find scans for his physical feats/abilities. Regarding his intellect, it's usually just said in comics that he studied the sciences, criminal psychology and learned detective skills.
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