Battle takes place in Gotham City. Battles are won by KO or death.
Round 1- Black Widow needs information from the Joker. See's unable to physically harm the Joker. Does she get the information. (Similar to how she got the information from Loki in The Avengers.)
Round 2- Both get a week of prep.
Round 3- Black Widow is in the same situation as Batman in the TDK. Will she able to find the Joker and kill him.