This MU is really really hard for 'zard.
Steeler covered pretty much all I wanted to say on the matchup already, but it is insanely difficult.
Turnips keep him out pretty bad and he's big and easy to combo. He's one of Peaches easiest matchups and anyone that knows it can rock your socks hard. The best piece of advice would be to be good at reading and avoid shield pressure at all costs, also always recover low and abuse invincibility of dragon rush to break shield pressure, peach isn't super fast and it sometimes works. Also peach is light, so dragon rush can be a good mixup if not expected and can kill surprisingly early. Just watch out for Fair, if peach is in the air, and hits you with a turnip, you'll most likely get hit with it, and it kills heavies at about 120%
Also if you're feeling gutsy, you can dragon rush off the edge and try for an early kill.
At least Zard is immune to the infinite. =/