You have to realize that Peach's priority is absurd, and so if you try trading hits with her, you will not win. Ever. That being said, your Nairs were very ineffective here. You used them to try and not get hit by Peach's attacks, which is reasonable, but in doing so you built up 'pointless damage'. Basically, you hit Peach so much that performing combos on her afterwards became a chore instead of an activity. I suggest using them more wisely, and reserve them for when she's floating in the air, as they are all too easy to CC.
Second of all, the DI coming from both of you was horrid at times. If you want to live, DI up sometimes
Third of all, you are not going to beat a Peach on the ground. She is too powerful there. The only way you'll win is by luring her into the air, or forcing her there, and smacking her around with good spacing. Her Nair will take out anything you have if you're in its range, so keep that in mind. Stomp comes in handy when you're trying to get her out, however, I would suggest spacing it. Land behind her if you can because her grab range is pretty good. Don't fastfall it because you'll get hit by a dress and won't get the stomp off, if anything just direct yourself away from retaliation.
Never, EVER land in front of a good Peach. If you do, roll away ASAP before she grabs.
Oh yeah, and you need crisper combos. You'll have a hard time edgeguarding Peach, so always try to outright kill her instead. Dthrow Knee is an obvious choice, or Dthrow Uair Knee. Dthrow to Nair and Uair chains work very well at low %.
Hope this helps.
