Duck and walk. It's painfully slow and incredibly frustrating, but you have to do all you can to get them in the corner and punish them if they try to run and switch sides on you. Even the best zoners can be backed into the corner and mixed up a couple of times for 800+ damage. Save your meter for combos since MB roll will usually get punished vs Deadshot, Fate, Batman, etc.
Where I have the most trouble is characters who can zone & have tons of air mobility (Supes, Starfire, Cyborg). These are by far some of his worst MUs because they can zone you from an area on the screen you cannot well attack. These are your MB roll matchups where you need to get a read, get in, and punish. Be patient. Don't be afraid of chip, and look for chances to air-to-air, up vines, or D2 them. It's tough man, but be vigilant.