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During the Batman Beyond series, there's the episode Terry's Friend Dates a Robot during which you can see Bruce Wayne actually training him to fight against robots, in a simulated fight against some of Bruce's old rogue gallery (The Riddler, Two Face, Killer Croc):

Also, in episode Curse of the Kobra, Bruce also sends him into meeting with Kairi Tanaga, whom Bruce knew from when he trained with the same master before becoming Batman, so that Terry could learn to fight more efficiently:

It's more than likely that Bruce would continuously train him into becoming a better Batman, in order to increase his likelihood of staying alive.

It's questionable whether or not he became a master in martial arts like Bruce was, but we get a glimpse of how easily he took care of Shriek in the Justice League Unlimited episode titled Epilogue, when he became a grown up man, long after the timeline of Batman Beyond:

On a more trivial note: there used to be a video on Youtube showcasing how Bruce (as Batman), always took out enemies coming from behind him by hitting them with his fist (which the video called his signature move). In a Batman Beyond episode, as Bruce was tending Terry's wound, the latter complained that he doesn't have eyes in his back.

Later on, in an unidentified sequence, Terry (as Batman) knocked out a bad guy who tried to jump him from behind, showing he actually learned from Bruce.

During the Batman Beyond series, there's the episode Terry's Friend Dates a Robot during which you can see Bruce Wayne actually training him to fight against robots, in a simulated fight against some of Bruce's old rogue gallery (The Riddler, Two Face, Killer Croc):

Also, in episode Curse of the Kobra, Bruce also sends him into meeting with Kairi Tanaga, whom Bruce knew from when he trained with the same master before becoming Batman, so that Terry could learn to fight more efficiently:

It's more than likely that Bruce would continuously train him into becoming a better Batman, in order to increase his likelihood of staying alive.

It's questionable whether or not he became a master in martial arts like Bruce was, but we get a glimpse of how easily he took care of Shriek in the Justice League Unlimited episode titled Epilogue, when he became a grown up man, long after the timeline of Batman Beyond:

On a more trivial note: there used to be a video on Youtube showcasing how Bruce (as Batman), always took out enemies coming from behind him by hitting them with his fist (which the video called his signature move). In a Batman Beyond episode, as Bruce was tending Terry's wound, the latter complained that he doesn't have eyes in his back.

The DCAU fandom does have a list of the times Batman performs the offhand backhand as described above. Two of them happened when:

• A henchman of Mr. Freeze attempts to sneak on him from behind in episode Heart of Ice from Batman: The Animated Series.

• Mercy Graves attempted to shoot him from behind as he snuck on a sleeping Lex Luthor to interrogate him in the second part of episode World's Finest from Superman: The Animated Series

This was the scene I was referring where Terry told Bruce he doesn't have eyes in his back, when the latter asked him why he wasn't watching his back. It happened in episode Payback from Batman Beyond:

Bruce: Why weren't you watching your back?
Terry: I was too busy watching my front! Am I supposed to have eyes everywhere?
Bruce: Only if you want to live to a ripe old age.
Terry You don't make it sound too inviting.

Later on, in Batman_Beyond: Return of the Joker which happens after the events of Batman Beyond, Terry (as Batman) does it to a villain named Ghoul who tried to sneak up on him from behind, which means he probably learned the move from Bruce, or learned to watch his back as he was told.

And at the beginning of the final episode of the DCAU continuity, titled Epilogue from Justice League Unlimited, a grown up Terry also does it again, this time against a security guard approaching him from behind as he's sneaking into a highly secured home.

During the Batman Beyond series, there's the episode Terry's Friend Dates a Robot during which you can see Bruce Wayne actually training him to fight against robots, in a simulated fight against some of Bruce's old rogue gallery (The Riddler, Two Face, Killer Croc):

Also, in episode Curse of the Kobra, Bruce also sends him into meeting with Kairi Tanaga, whom Bruce knew from when he trained with the same master before becoming Batman, so that Terry could learn to fight more efficiently:

It's more than likely that Bruce would continuously train him into becoming a better Batman, in order to increase his likelihood of staying alive.

It's questionable whether or not he became a master in martial arts like Bruce was, but we get a glimpse of how easily he took care of Shriek in the Justice League Unlimited episode titled Epilogue, when he became a grown up man, long after the timeline of Batman Beyond:

During the Batman Beyond series, there's the episode Terry's Friend Dates a Robot during which you can see Bruce Wayne actually training him to fight against robots, in a simulated fight against some of Bruce's old rogue gallery (The Riddler, Two Face, Killer Croc):

Also, in episode Curse of the Kobra, Bruce also sends him into meeting with Kairi Tanaga, whom Bruce knew from when he trained with the same master before becoming Batman, so that Terry could learn to fight more efficiently:

It's more than likely that Bruce would continuously train him into becoming a better Batman, in order to increase his likelihood of staying alive.

It's questionable whether or not he became a master in martial arts like Bruce was, but we get a glimpse of how easily he took care of Shriek in the Justice League Unlimited episode titled Epilogue, when he became a grown up man, long after the timeline of Batman Beyond:

On a more trivial note: there used to be a video on Youtube showcasing how Bruce (as Batman), always took out enemies coming from behind him by hitting them with his fist (which the video called his signature move). In a Batman Beyond episode, as Bruce was tending Terry's wound, the latter complained that he doesn't have eyes in his back.

Later on, in an unidentified sequence, Terry (as Batman) knocked out a bad guy who tried to jump him from behind, showing he actually learned from Bruce.

During the Batman Beyond series, there's the episode Terry's Friend Dates a Robot during which you can see Bruce Wayne actually training him to fight against robots, in a simulated fights against some of Bruce's old rogue gallery (The Riddler, Two Face, Killer Croc):

Also, in episode Curse of the Kobra, Bruce also sends him into meeting with Kairi Tanaga, whom Bruce knew from when he trained with the same master before becoming Batman, so that Terry could learn to fight more efficiently:

It's more than likely that Bruce would continuously train him into becoming a better Batman, in order to increase his likelihood of staying alive.

During the Batman Beyond series, there's the episode Terry's Friend Dates a Robot during which you can see Bruce Wayne actually training him to fight against robots, in a simulated fight against some of Bruce's old rogue gallery (The Riddler, Two Face, Killer Croc):

Also, in episode Curse of the Kobra, Bruce also sends him into meeting with Kairi Tanaga, whom Bruce knew from when he trained with the same master before becoming Batman, so that Terry could learn to fight more efficiently:

It's more than likely that Bruce would continuously train him into becoming a better Batman, in order to increase his likelihood of staying alive.

It's questionable whether or not he became a master in martial arts like Bruce was, but we get a glimpse of how easily he took care of Shriek in the Justice League Unlimited episode titled Epilogue, when he became a grown up man, long after the timeline of Batman Beyond: