Val Kilmer in
Top Secret!:
And this dance:
YouTube - Top secret! dance scene 
Regarding Classical music, I suppose there are many parodies. I remember a movie named
Off Key, with Joe Mantegna, George Hamilton and Danny Aiello, which is a parody of Opera singers, but I haven't found any video on YouTube.
Florence Foster Jenkings doesn't count, because she didn't intend to make a parody, although the results were obviously disastrous (just listen to
this). In fact, believe it or not, she thought she was a good singer.
