My advice, don't bother. Just buy sulfuric acid from someplace.
My reasons for this are:
a) sulfuric acid is very corrosive, good luck with any type of distillation
b) cadmium tends to be in those batteries, and cadmium is toxic and can be absorbed through the skin
c) there is lead and lead sulfate, lead sulfate can be absorbed through the skin I believe
d) risk of electrical shock or possible battery explosion in the event of a short circuit