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I searched "fight set to music on stage" and came up with the trope index Fight Scene. This lists a variety of tropes seen in duels, melees, and battles. Take a look and see if anything fits your needs.
I guess Ballroom Blitz or Bar Brawl inch close, but they seem to be distinct, respectively on the impact of breaking a high-class event, and the latter focusing on the destruction of the enviroment rather than the fighting itself.
Considering what I'm looking for is also present in Katana ZERO, and Invoked in Payday 2's Nightclub on Loud, this might be worth a new Trope.
Oh! Sorry, there's no budget for a signature.
Oh, here we go! Orchestra Hit Techno Battle is what I'm looking for.
Oh! Sorry, there's no budget for a signature.
Great!
Not to be confused with Dance-Off, we're talking actual violence that just so happens to take place on a spiffy stage with energetic music. Best descriptor would be Thouzer's boss battle in Fist of the North Star: Lost Paradise .