What you want to do first is stop their turnip game. You can do this by staying just outside of anything they can do to you, but within threat range, so they can't pull turnips before you can hit them. Turnip pulls are actually pretty slow, so it's not too hard to do.
Then, shut down everything else they can do. Peach is a very slow character. Her float is slow and so is her run. So just space yourself out, don't use anything overly laggy and you'll completely take her apart. Watch the falling fair though, it's got a crazy hitbox that hits like right below her at some point.
Grabs work really well against Peach, as she's floaty, so you can catch her and finish with an fsmash or utilt or something along those lines. Ken Combos work too. Mostly, you'll want to keep her above you, as her options are severely limited there, since her dair has no priority and she can't pull turnips there. If she floats around, just follow her.
If she manages to grab you, look at your percent. At higher percentages (like over a hundred), expect the fthrow. DI up and towards so you don't die. At lower percentages, watch for the dthrow. DI down and behind her so you don't get combo'd after it.
If she manages to pull a turnip, nair through the throw. If she pulls a scary turnip, don't be afraid. Just keep hitting her, and try to avoid getting hit by the turnip.
If you're recovering against Peach and she's standing on the ledge, tap L or R as you're rising with the Dolphin Slash and you'll tech the dsmash if she uses it. It's pretty easy to do. Also, if she throws turnips, save your double jump and try to avoid them the best you can.
Oh yeah, and don't crouch cancel the dsmash.