In their very first encounter, Dracula wipes the floor with Batman, almost nonchalantly so, even. He barely has to do any real fighting, and when he does dodge Batman's garlic-laced batarangs, it's a simple bend or shift to the side, like they're no real threat to him. And when he actually gets his hands dirty, it's freaking brutal. A single shove to the chest pushes Bruce back several feet and into a brick wall hard enough to shatter it, slamming him headfirst into the ground cracks the pavement with enough force to leave an impact crater (which, Batman's ability to take that hit is also a moment in and of itself, as that would kill a lesser man), and it's implied that he was holding back! There's just this overwhelming, eerie, chill-inducing sense that he has total control of this entire encounter. His violinLeitmotif even overshadows Batman's guitar leitmotif several times during the fight, if only to undercut the creepy, terrifying tone of the scene as he very nearly bests the Dark Knight and makes him one of his legion of the undead. If it weren't for the sunrise, Batman would have become a vampire as well.
Dracula: You have no concept of the harm of which I am capable.
Batman triggers the machine, and blasts Dracula with artificial sunlight. As Dracula is burning, he watches Batman, who is standing between him and the rest of the light, and realizes his identity.
Dracula: You are...Bruce Wayne?
Batman (opens his cape, making his shade look like a giant bat dominating the kneeling vampire): I'm the Batman...and you're dust. (jumps away, fully exposing the light, which instantly kills Dracula)
That's not entirely accurate: he pulled himself up with a grapnel, let the UV light burn Dracula, then came down on top of him and shattered his burning bones with one punch!
Also during the final battle, at one point Dracula has Batman on the ropes. That is, until Alfredshoots Dracula in the throat with the vampirism cure. It doesn't work.
Batman vs. the vampire army. Outnumbered by vicious, super strong and super fast undead, and with only a limited supply of cure for the people of Gotham, he still manages to beat them all. Badass Normal indeed.
The title itself is called "The Batman VS Dracula". need we say more?