Hang out under a platform and laser. If she's on the ground it keeps her grounded and unable to pull a turnip. Only way for her to approach is to float above lasers, but then she can't come down on you because the platform is there.
Camping top platform is very good because it takes Peach's double jump 9 years to get her up there. If you see her coming up you can short hop dair or just move to another platform.
Don't challenge her float. This is the most important thing. If she's floating don't try to jump in and hit her out of it, you will lose. She has to come out of her float eventually. If she's floating, dash away, then when she drops down, laser her and grab her. Uthrow always leads to something.
Don't nair her, because you'll get crouch-canceled. Dair combos well. The best way to combo her is to like, dair, then instant double jump, to fast fall dair.
With edgeguarding, use lasers and threaten with bair to force her to go low, then try to grab edge. A lot of the time though you have to respect her and let her grab edge. Luckily Peach has bad options when on the ledge. Just space yourself on center stage so you don't get get-up dsmashed, and laser.
Laser jab is good for opening up for a kill. You can laser jab, and if you jab her shield, dash away. If you laser jab and it hits, you can bair or sometimes fsmash for the kill. Just be careful not to do it at low percents or your jab will be crouch cancelled.
Falco/Peach isn't too bad. Not as bad as Falco/Samus.