The quintessential Batman musical (excluding Holy Musical B@man!, which I have not seen yet), still remains the Mayhem of the Music Meister! episode of Batman, the Brave and the Bold.
The music is actually incredibly catchy, the plot is the right kind of silly, the singing is on point, and the got Neil Patrick Harris to play an entirely new villain created for the show! Not to mention the fact that without spoiling too much, on his first ever outing the Music Meister actually comes closer to accomplishing his goals than I think half of all villains have ever come throughout their careers!