There are very few places that Batman is vulnerable. Ever. One place though is the realm of dreams, where once asleep, he has very little control over things.
One such villain that has caused problems because of this is Dr. Destiny, a villain who has the power to manipulate dreams in such a way, that it can kill the dreamer if the stress becomes to high.
In the Justice League cartoon series, Dr. Destiny almost single-handedly took out the Justice League by using their dreams, or in this case nightmares against them. It was only after a combined effort between Batman and the Martian Manhunter that the teammates were saved, and Destiny stopped. For Batman, he did everything he could to stay awake, to not allow Destiny the chance to take over his dreams.
Eventually, he took down Destiny, and proved once and for all, that awake or asleep, you don't mess with Batman.