Damian, trained from birth in the League of Assassins, is an incredible dancer. He was trained to have total control over his body, and one of the best ways to learn that is dance styles like ballet, swing, belly dancing, pole dancing, etc.
The batfam slowly finds this out over the years. Apart from Jason and Cass, as they have the same training. Eventually Tim finds out from his time with the League but that's after a couple years of knowing Damian.
The first is the obvious, waltzing at galas. That's expected, of course Talia would teach Bruce Wayne's son to waltz.
The family goes to one of his school events, and are very surprised to see him doing ballet (Cass and him practice together and she was happy she could share this with her shocked family).
They find out he can swing dance while undercover at some speakeasy club. Tim is undercover as Caroline Hill (and this is post League base explosions), and absolutely has a shit eating grin on his face when he sees Steph's flabbergasted expression across the bar. He later tells her Damian is who taught him to swing dance actually.
Dick tries very hard to forget finding out Damian could pole dance, having been visiting the Iceberg Lounge and not knowing Damian was undercover to keep an eye on a new Penguin deal. He's just glad he's an adult now cause he doesn't think he could bear watching his brother doing that underage without blowing his cover.
Jason and Damian end up undercover as belly dancers for entertainment at some rich fucks compound so they could bust his trafficking ring. Duke still can't forget how mesmerizing they both were (and maybe asks them for tips later, as well as telling Tim the latest batch of Bat™ concealer hid the scars so well he almost didn't believe it was them).
Babs blows everyone's minds when she sends a video of Damian break dancing to the group chat, cause even the League trained bats didn't know he could do that, and Damian just smiles and says he picked it up from watching tiktok videos Jon sends him.
Bruce had always guessed what Ra's and Talia had taught Damian, but each discovery he couldn't help but be amazed and impressed with his son. He pays Babs for videos of his dancing to save in his Proud Dad™ folder.