Maybe I'm being completely stupid about this, but I can't beat challenge mode.
Not that I can create a normal win, I can drop my opponents to ridiculously low life in the negatives (went to about -450 with annihilus), but the game just keeps moving forward. What am I doing wrong?

There is probably a certain objective you need to reach that you're missing. The mission Final Showdown? has having to KO Mr. Sinister before you can win.

See, I thought that too, but all I can find is that challenge mode is a best of one game - I can lose it by losing the standard way, but I can't win for some reason. If there are objectives, I don't see them anywhere.

You could have a bugged copy. Seems to be a few of those going around.