I'm a martial artist and a bit of a nerd and I hear a bunch of people try and list out what arts he knows but I have spent time just watching Batman's choreography throughout the 4 games just to do this. This shit took me a while I'm not gonna lie to you. Also I try to avoid too much overlap in technique so while he may do a move that exists in a certain style, it's not predominant enough for me to consider adding to the list.

Batman shows physical art usage of

Panantukan

Kali

Judo

Karate

Aikido

Ninjutsu

Hanbojutsu

Shurikenjutsu

(I'm not adding each individual "jutsu" subsection that can be lumped in with Ninjutsu, though I'd like to highlight his use of Intonjutsu, Shinobi Aruki, Shinobi-Iri, and Hojojutsu)

Iaido

Taekwondo

Taekkyeon

Hapkido

Kung Fu (This includes Tai Chi. If you wanna know why I put them together it's because Tai Chi is meant to be "shadow boxing" for Wushu (the more accurate name for Kung Fu), not its own self defense discipline.)

Muay Thai

Muay Boran

Lethwei

Silat

Krav Maga

Base Jumping

Parkour

Gymnastics

Boxing

Wrestling (Greco-Roman style seems to be pretty predominant)

Catch Wrestling

Brazilian Jiu-Jitsu

Capoeira

(I mean his accuracy with the REC also suggests he's good with firearms and in the comics he's one of the world's top 10 Marksmen so I suppose we could add this)

And as for non-physical knowledge he has we have: Cryptography

General Chemistry

Advanced Biology

Anatomy

Advanced Physics

Mechanical Engineering

Electrical Engineering

Civil Engineering

Tactical/Defensive Driving

Piloting

First Aid

Tracking

Computer Science

Criminology

Ballistic Forensics

Forensic Pathology

Forensic Toxicology

Digital Forensics

Data Analysis

Bioinformatics

Data Science

Networking

And thats all I can think of. Idk why I decided to do this but uh here.