Cover platforms to punish her if she lands on one. Keep menacing the high route in general, and get her to recover low. You can even give her the ledge : she's not a spacie with invincible ledge-dash. Peach has a hard time getting on stage from the ledge, just watch out for -let go of ledge>immediate airdodge onstage.
Don't challenge peach parasol, it will eat everything. Instead press her to do something by shooting lasers, and take away her float by the way. If she can reach the stage without up-b, watch out for nair, fair, airdoge, and punish her landing.
OR you could do it like sandstorm westballz : scarjump > dair for the ultimate style points falco dunk.