Batman without prep time is still A-tier dude
Batman without prep struggles with any martial artist who has better stats (but less skill) than him, and has a losing record against martial artists from Black Canary's skill level on up.
note that this doesn't count a drunk and elderly David Cain.
Natasha is between Punisher and Wolvie/Cap/Panther stat wise and prolly on par with Nightwing skillwise, but has about 80 years experience, the greater majority of them being a "villain".
I'm not saying she's walk all over him, but a fight with Natasha is a losing fight for Bats.