Generally, Peach is bad vs retreating aerial pressure and AC bair, but you want to have a fair bit of stage to do retreating lasers or retreat when she's setting something up. You don't want to be too obvious or pre-emptive with these, lest she attempt to dash attack you for it.
vs. Float
Observe her height, current momentum and relative positioning, and any moves she's doing currently. If she's not doing a fair yet, you can actually probably challenge the float when it's not grounded. Depending on height, you could go for a nair, fair if slightly higher, or uair if slightly higher, all shorthopped, and used at angles her moves don't work well against yours. Only do these if she is not starting a fair, and not able to avoid given her current momentum and position. The exception is uair. The move is huge, and if she's high enough above you but close enough horizontally to not avoid it while retaining the float, you can pretty much uair at no consequence (this height will be above sh laser height). If you connect with the nair or fair at zero, try to delay them a bit and IMMEDIATELY shield, dash away, roll, or utilt depending on whether what you think you have time to do without getting naired, unless she gets carried with the aerial right to where you're landing, in which case, shine no matter what. If you shield, you may wish to shield DI in and shine if she does it higher up, or out and try to reset the situation or AC bair if she does it lower. If you dash away, you can get many things, including a grab, a bair, pivot fsmash, a dair or any other number of good things. If you're not confident that you can hit Peach in the earlier parts of a jump, and she's at a height where you can't ftilt her out of float, it may be best just to roll or wavedash in whatever direction gets you farthest from where her current momentum would have her land if she stopped floating just then; the only thing that might get to you fast enough to punish the roll is dash attack, and even then, probably not. You can also run wavedash or walk under her when she does an advancing float from higher up, which also means a free bair, fsmash, or utilt if she attempts any aerial (and bair and utilt allow you to punish landing even if she airdodges). You can also do a laser to space outside of fair range always, and if she doesn't SDI, it's a free ftilt, utilt, or fsmash. If she's floating at a more grounded height, you can obviously just laser, but she can just land and start doing grounded options very quickly, but because this is a bit of a mobility commitment if she doesn't use her double jump, you can usually setup an approach or space an ftilt. Although you shouldn't try this, if she is floating above laser height, you actually has a decent chance of hitting her oos (Especially if you angle up and towards).
On the ground.
Peach's dash isn't very fast, and her only particularly fast option for farther distances in front of her is dash attack. If she isn't wavelanding off a platform, she can't move in the air very fast either (and there's very limited locations where she can do that on any stage). You can shield the dash attack and shield DI out as an option select for everything but grab, which will take much longer to reach you, and punish anything that isn't a float. Chances are, the Peach player isn't doing run up pivot AC bairs (which would still be slower than dash attack to get to your position) so you have time to recognize a float and attempt to counter with a laser, ftilt, aerial, or DD. If there's platforms, you can fulljump away and she doesn't have much ability to chase this. When she's sheilding, retreating aerials do wonders as none of her faster oos options have particularly good range in front, and you can bait out and punish almost everything. Generally, try to avoid the range of the options that aren't dash attack, and if you don't see her attempting them, you may wish to shield because she's probably trying dash attack (or dsmash, which you can shield DI and punish). Otherwise, you can wall her with ftilt if she keeps moving forward with any thing but shield (though if she expects this, she can punish it, so mix in aerials and even jab if she isn't representing CC or is at higher percents), and laser her from farther so you don't have to deal with this. If she rolls away, you can sh laser towards and try to space at around ftilt distance. Laser dtilt is extremely annoying to her, and while you should just grab her dair her or AC bair her most of the time if she tries to get in position to land a Dsmash, you can charge one of your own, and because Falco's legs are invincible, you can avoid her Dsmash and hit her with a charged one for attempting it. Try not to act to pre-emptively after challenging her shield either by hitting it with a laser or just seeing it, if you wait and react while maintaining proper spacing, you can deal with everything and get better punishes easier.
Punishes (onstage).
Uthrow leads to good things, including fairs or uairs depending on DI and percent (uair had a huge percent range), try to be fast-falling as you hit with dairs for pillars, and hit with the earlier hitbox (of course, in NTSC, you can also go for AC dair, which you should still be falling during). She get's pillared and pillar tech-chased like a floaty, pretty simply. While I already mentioned aerial utilt or shine followups in the previous section, if you're landing on a lower platform, utilt can serve more as a frame trap, where even if she doesn't drift into it, you can punish her double jumping or airdodging, but don't utilt until she's close enough for it to hit if she drifts into you any more. When done and Peach is lower to the ground, she can hit the floor, and if she misses the tech, it's a free utilt, shine, dtilt or dsmash, depending on what you prefer, and the first three can all set up for that like dtilt as well. If she techs through you, free fsmash, aerial into combo, grab, whatever. If away, you can try to be safe and laser, but you can potentially wavedash or pivot fsmash, or grab or get an aerial. If Peach holds down, she hates downtilt, downsmash, and utilt (though she's not a big fan even if she doesn't). At higher percents, bair, ftilt, and fsmash also make crouching a nightmare for her. If she's DIing out, it may be more desireable to dtilt or grab after a dair than shine, or turn away from wherever she is->utilt. You can use movement to stay beneath peach when you get her in the air and just harrass her with uair, utilt, and bair. If she tried to airdodge through an upsmash, she probably gets hit by the end anyway.
Edgeguarding.
Don't laser her up-b unless you can land a normal attack right afterward. If you walk up to the ledge and slide into a downsmash, it pretty much won't get hit by up-b, and punishes when she fails the sweetspot, though you can also just judge her position relative to the ledge. If she's low enough that she has to up-b, and would either have to grab ledge or barely go above it, but also far enough that it can't hit, grab ledge from the ground on stage, probably with a wavedash or PC drop. Refresh invincibility no more than once, and do so before she can hit you at the ledge if she can. If she is barely able to get above, you can try to dip low and ledgehop bair/dair, shine-turnaround dair, or do a higher ledgehop dair not going onstage, but able to fire-bird to the ledge. Do whichever will hit, but won't let the Parasol hit you. Alternatively, generate enough threat that she doesn't go for on stage and just hold ledge and roll as your invincibility is ending. If she's too low anyway, easy, refresh invincibility if you have enough room (you do), roll. If she's close enough she could hit, you may wish to do a slightly pre-emptive fullhop, or short hop if you can get far enough behind the Parasol, and just grab ledge while she's still rising, or if she didn't Parasol yet, immediately refresh, or attempt a ledgehop nair or dair if you don't think she'll tech (land back on stage). Ideally, you don't attack, and just casually roll back on as she drops to her demise. You can generally laser her a lot from farther offstage, or if she attempts a get up option, and eat jumps/float. Laser dsmash, laser ftilt, and laser fsmash are all things she doesn't want to get hit by, but you can also just do bairs or utilts depending on where she'd have to airdodge, as even if they miss, you can punish the air dodge. She has very limited ability to recover from offstage dairs, but be weary if she has her float, as it makes it easier for her to hit you out of all of these walling moves.
Other stuff: Peach sucks vs platform camping. When you get to percents where shine to shine doesn't connect because it sends her too far, shine uair will usually KO. If you give her room to pull a turnip, you can pressure her without having to worry about grab. Off of fthrow, anything it looks like it should from a standing position towards the middle of it's hitbox pretty much will if you do it immediately. After uairing her on a platform, say out of uthrow, utilt. After fairing to a similar position, shine. Flying at an aerial Peach (preferably in hitstun) who's low to the ground and at the edge with a dair either sends her off, or gives you an extremely easy tech-chase. Play lame and Peach has a very hard time, she can't really outlame you. If you get dthrown, DIing behind makes it hardest for Peach to cover all tech options on a flat area. Always punish a roll through you if she attempts one. If you're already doing an aerial and it misses, just DD punish, shine or utilt and it will usually work out.