I play against a friend of mine very regularly who mains Pyrrah, and after playing for months he's gotten very good at punishing Maxi, JGing all the basic strings, all that. What you sort of have to do is be patient and play a whiff punishment/punishment game of your own and scale back the aggressiveness. Even if you get predictable with safe pokes (say on wake-up) that mess will just get JG and you'll get his with a disproportionate amount of damage in return.
Basically unpredictability and whiff punishment are your friend. You can get away with certain mix-ups, especially ones that are a little more unconventional than 1B mix-ups. Try things like 4B and mixing that with LO B and LO K and see how they react. If they always JG something like 1B RO AK (rather than ducking) just stop the move and grab them. Grabs seem to be your best friend against people too focused on JGing.