Though associated with Green Arrow many times, Count Vertigo has come into conflict with Batman often. Sometimes even being associated with the League of Assassins or the Suicide Squad. Though it's changed over the years, Count Vertigo's most powerful ability is to induce Vertigo on any in his sight or area. For one who prides himself on balance and precision, like Batman, this can be a big problem.
Despite this, Batman was able to trump Vertigo many times, in one instance, actually closing his eyes and sensing the dangers around him, and avoiding every single one. Still Vertigo has proved to be a worthy adversary, and more than capable of testing Batman's skills.