one thing i've noticed about Greinke (i've watched almost all of his starts since I have the MLB TV Premium package), is that he gets so many hitters out on that hard slider down and in to lefties and down and away to righties, that pitch appears as a strike and is never one
he never throws that pitch in the beginning of a count, he always throws a 4 seam 95-96mph fastball on the corner and sometimes over the plate for a strike, when hitters are down 0-2 or 1-2, he starts throwing that devastating slider
this is a situation of course where, to be successful against Zack, you need to stop trusting your eyes on 2-strike counts and start analyzing the count your in and what pitch to expect instead, work the count to 2-2 or 3-2 and try to get him to feature something in the strike zone (his curveball or that mid-90's 4 seam fastball)
against our lineup, i think a pitcher like Zack would rather walk a bunch of guys and try to get out of a 2-on or bases loaded jam, because his stuff is so good rather than throw hittable pitches on 2-2 or 3-2
with that said, it's easier said than done of course, i'm not speculating as to finding the key to beating Zack, but it pretty much is the solution. executing that will be the challenge of course