This sort of thing is generally pretty easy. For instance, this would be a good start:

    for i in {0..10000}; do
       wget http://whatever.invalid/genres/$i
       sleep 1
    done

From there processing the results to pull out the genre would be a regex away; a single properly formed grep could probably do it.

Determining the top number would have to be done by hand; having holes in the sequences makes it more complicated but you could still use a sort of basic binary search.