Motoko easily overpowers Batou by constantly hacking into his eyes and slowing down his sense of perception by about half a second, which comes in quite handy when he drops his gun and that extra split second gives her the chance to grab it first.
Motoko: "I always told you your sleepless eye was too easy to infiltrate."
When the 78th Ranger Unit takes control of the city's traffic system, the Major maintains control of her bike and pulls her sidearm as she figures she's going to be attacked. Indeed, when a large van pulls up next to her and the door opens, she nails her first would-be attacker in the head before he can even bring his gun up. Then when another shooter brings out a gatling gun against her, she jumps her motorbike through the van's open door and slams the guy against the other side. And while still in mid-jump through the middle of the moving van, she meets eyes with the driver, Batou, who pulls his own gun, and they still manage to trade shots with each other before her bike busts out of the other side of the van. Damn.
After Saito defects to Batou thanks to Batou paying him triple what Motoko was offering him, he shows up in a helicopter to cover Batou during the highway chase and gets her lined up in his sniper rifle's sights. He loses sight of her for a moment when the Logicoma moves behind Batou's van... and the moment she moves back in sight of him, she's pulled out a rocket launcher.
The second fight between Motoko and Batou. He actually starts off by hacking her so she sees a fake image of him laying dead in the truck. Clearly he learned from their last encounter. And it takes Motoko, Paz, and VV all working together to subdue Batou.
Then after receiving the antivirus that shows him the truth of what happened in Qhardistan, Batou returns the favor by using the Logicoma's twin machine gun to destroy VV before she can kill Motoko.