I honestly don't see the Bat-Family winning this. They can probably take out Beast or Cyclops, but Nightcrawler? Nope.
Oh, and the reason I say Beast is because, even though they're not as fast him, they do have gadgets that can mess with his senses and can double team him if needed. I'd put Dick and Tim on him and they can do something.
With Cyclops, It's a matter of getting in close. Batman can use the walls, trucks and his gadgets to his advantage to close in on him. We all know Batman is known for doing great things with what he has. Once he gets in, He can go H2H with Cyclops and eventually take him down.
Nightcrawler is the reason they'd win IMO. He doesn't have to stay where he is. He can just teleport around Damian and piss him off and eventually take him out. From then on in, he can just help who needs it the most. BUT if Dick and Tim or Bruce finishes their fights before Nightcrawler does, They can win.