I saw a lot of shffled nairs in place. Don't do this if you're playing a Peach. It'll only get you grabbed. If you're going to nair, try to make sure you have some momentum behind you so that you land behind her shield.
Like Sudai said, needs moar shine combos. Take advantage of Peach's perfect slide distance and waveshine combo. When you're edgeguarding (in my personal opinion), it's best to hang on the ledge and drop down, then jump back up with a bair so that you can get right under her umbrella. If she runs into you with it while you're hanging and knocks you off the ledge, you're going to get bounced off the stage with a d-smash (providing you don't tech, of course).