I personally think Genie can do it, but this isn't the battle forums so this is okay, right?
If we take highest end feats (which would be Duck Amuck) than the answer is nobody. Bugs Bunny is the single most powerful character in all of fiction, with the possible exceptions of Goku, cutscene Dante, and Batman with prep time.
If we take low end feats than Robin is more than enough.
Bugs Bunny isn't meant to be used in battles.
Bugs Bunny is great, don't get me wrong. But he won all of his battles because he was supposed to, simple as that. This guy sums up situations like this better than I could, though:
I was actually about to post this on almost every battle forum battle but you beat me by putting here...
To those bringing up the Gremlin and Cecil, should remember that was Bugs when he was very early in his appearances(early 40's, 41/43 to be exact) if you take prime Bugs Bunny then that would have different outcomes, besides Bugs already beat Cecil anyway in their 2nd race, the 1st race Cecil cheated with his 8 cousins so he didn't really win anyhow.
With the Gremlin, Bugs had yet to become the smart, clever rabbit that everyone knows(by comparison of later appearances.)