Is it correct to say "…battle between x versus y"?

Technically speaking, the phrase should have been either

The battle of X versus Y

or

The battle between X and Y

I think it's more common to say "The battle of (placename)" or "the battle between x and y" instead of "the battle of x versus y", but I'll have to let someone else try to NGram that up.

However, I'm guessing that you were watching a show called "Man versus Food", and the host of the show isn't about to miss a chance to slip the name of the show in even if it makes the sentence sound a little funny.

Here's some Ngrams that show "battle between X and Y" is much more common than both "battle of X versus Y" and "battle between X versus Y", which you can't even see above the zero baseline: