^ Right. Almost every department has one or more Shakespeare specialists; when you're doing research, you should look into what specifically professors at specific schools are interested in. For example, at the school where I earned my doctorate, the Shakespeare professor in the English department wrote about philosophical interpretations of the plays. So, someone who was interested in performance studies probably wouldn't do well there, or even be admitted. Try to find a few schools where the folks on faculty have similar interests to you. Figuring out what Shakespeare scholars have interests that align with yours--and what schools they're associated with--is probably the best research approach you could take.
As far as entry requirements go: you'll need to take--or retake--the GRE general test, and for most PhD programs in English, you will have to take the Literature subject exam. You'll also need a writing sample: for most schools, this will be a 15-20 page, publication-quality essay on a topic in your area of expertise. If you don't have an article-length paper ready to go right now, you should start one ASAP. (I imagine theatre studies PhDs would require both the GRE general and a writing sample, as well)
I hope this helps. There is a lot of competition to get into advanced-degree programs these days, so best of luck to you.
"You travel alone because other people are only there to remind you how much that hook hurts that we all bit down on. Wait for that one day we can bite free and get back out there in space where we belong, sail back over water, over skies, into space, the hook finally out of our mouths and we wander back out there in space spawning to other planets never to return hurrah to earth and we'll look back and can't even see these lives here anymore. Only the taste of blood to remind us we ever existed. The earth is small. We're gone. We're dead. We're safe."
-John Guare, Landscape of the Body
