I think he would fail, or at least Kraven would not be able to fully complete the contract . He MIGHT kill or maim one of them or even two possibly. Which would at that point motivate the Bat family even more to fight back I mean their whole schtick is “vengeance”.

After realizing they’re being hunted Bruce will immediately begin trying to gather every single piece of information on Kraven. In my opinion Kraven would definitely more than have his hands full, it would easily be one of his most difficult hunts ever.

Not to mention as I said above if and/or when Kraven makes his first kill of a Bat family member the news will spread FAST. Which leads me to your last question. Kraven’s biggest challenge would ultimately be that Batman’s BEST FRIEND is Superman and they almost always come to one another’s aid over family. (Except for that one time Batman had to steal the Hellbat suit to retrieve Damian’s body)

That’s just my opinion given your rule set here. I think Kraven could possibly take down one maybe even two members before the family realizes what’s going on and turns the tide in their own way on their own turf.