This is actually one of my favorite matchups in the game, so excuse me while I word vomit at you a bunch of things to keep in mind about it.
Pt. 1 -- Win Conditions
You pointed out, quite well, that Falco needs to win neutral many times whereas Peach can get by with stray hits or trades. You are correct...yet this is also the same case in the Peach-Puff matchup, but that matchup is considered wildy lopsided in Puff's favor in spite of Peach's wincon being the same. Why is that? Well, there's the disparity in punish game, for a start. Peach can't really combo Puff off of her trades and stray hits, so she's forced to get more of them in the course of a stock, whereas with Falco she can rack up damage nicely. So that's gotta be your first mission as Falco: make her get more trades and stray hits per stock in order to kill you. You need to work on your escape game. I'll go into that in detail in the next part. Once you're at the point where Peach needs at *least* 3-5 neutral victories to beat you per stock, then the matchup evens out well. Why? Because just like Puff, you have all the tools at your disposal to win every single neutral interaction against her. There is nothing Peach can do that you don't have multiple answers for. Getting cc dsmashed? You have both dair and shine to deal with it. Getting fc fair->grabbed? You have uptilt, shine oos, upsmash, and a litany of other options at your disposal. Everything she does, you have an answer for, so winning neutral is more about identifying when a good peach will go for certain things, and then playing around it. I'll go into that in a later part. The basic win conditions are correct: You have to outright win neutral without trading or falling into a limited state of play. She has to trade and capitalize off your missed spacings to get damage. You need to win neutral between 5-8 times per stock, and you need to force her to win neutral at least 3-5 times per stock. The reason for this disparity is because while she hits like a truck, you have the better tools to win neutral. Played perfectly, you are capable of never losing a neutral exchange in a way Peach simply isn't. She *needs* those trades, you don't. This also slows the game down, so prepare yourself for that. She's a tank, she is capable of living for a long time, and even at 200%, if she gets one neutral exchange and you're at 0%, she could take that stock first if you aren't good at escaping what she's doing. Plan for the long game.
Pt. 2 -- Escaping Peach
It's critical that you don't let Peach kill you off one neutral exchange. As I just mentioned, that number needs to be at least 3-5 per stock; the nightmare scenario is that it's last stock, she's at 150% and you're at 0%, and she gets one good hit in neutral that leads to a kill. So you need to know the best way to escape her b&b stuff. Let's start with dsmash. If Peach is below ~50% and you come in with a dair, if that dair isn't the latest possible dair, she can actually jump into your dair and return to the ground, actionable, before you're able to act. If you dair too far into her that your shine after misses, then it doesn't matter how late it is, she can dsmash while you're in the jumpsquat/lag of your shine attempt. If you nair or bair while she's grounded, and she's below ~60%, she can cc dsmash as a punish before your shine comes out. If you uptilt and she's below ~60%, she can do the same. If you shine and she's grounded, she can jump, SDI the shine back into the ground, tech in place, and dsmash. After her fc aerials (especially bair), she can dsmash easily (all fc aerials are +4 on shield, fyi). If she's on a platform above you, she can dsmash and catch you trying to jump. She can dsmash after an upthrow at 0%. She can dsmash as a platform techchase, and on stages like FoD and PS, this can cover every option. That move has insane utility, but everything I just mentioned has an answer in neutral, and getting dsmashed in most cases doesn't mean taking 60% hardly ever. If you come in with dair, even if she's at 0, make sure it's the latest dair->earliest shine possible. If she does the thing where she SDIs the shine back into the ground and techs, doubleshine will beat it and pop her up. If you misspace the dair, you can skip the shine and just bail; if she's antsy, she'll dsmash, and then you can whiff punish. If you're not getting the latest dair and she's jumping into it, you can either nair (which will win and pop her up if she tries to jump) or hit her with shine instead and dj away (beware doing this on FD or when there's no platform nearby). If she tries fc bair-> dsmash, you can actually cc the bair and punish with shine, dtilt, charged dsmash (the legs are invincible and you won't get hit by the dsmash), dash back whiff punish, etc. Everything's got an answer. And if the dsmash is coming out, if you're shielding you want to shield DI away from her, and if she gets a hit on you, you want to DI up and behind her to get away with only a hit or two. And perhaps most importantly, if she lands on a platform and you're below her, there is no need for you to challenge her the moment she lands. She's got a hard time getting down on you, especially if you're right below her. If you wait, 9 out of 10 low & mid level peaches will panic dsmash. Simply bait, wait, and whiff punish.
What you want to focus on when getting out of her dsmash is not how easy it is or how often she uses it. What you want to focus on is her getting the least amount off of it, to the point where she can't really rely on it. If she's consistently getting 2 hits off of it, that's ~30%. That's the equivalent of a dair->shine-> aerial from you. That's three hits from your fair (which you can find more frequently than you'd think). That isn't something only she can do to you; you're capable of blowing her up just as well. It's when you jump into her dsmash on platforms, or you hold down while you're getting dsmashed instead of SDI'ing out of it, or you get techchased after it, that it becomes a real threat instead of just another one of her moves.
Beyond that, there's other stuff you should get good at. Chaingrabs on FD either need to end with you offstage <~50%, or with you in the middle of the stage at >~110%. Learn when to cc shine her weak dash attack (below ~80%). Learn how to challenge her float over your sh lasers. Etc. Learn to escape her stuff, and make her combo you a couple of times per stock, and this matchup really opens itself up.
Pt. 3 -- Your gameplan
Falco has a very straightforward high-level gameplan against Peach. There are essentially three parts of the matchup: when Peach is below ~40-50%, when Peach is between that threshold and ~100-160% (depending on stage), and the edgeguard. Part 1 is when she gets a lot off crouch cancel, and you can't really get true followups off of anything. Pillar combos won't work in this part of the gameplan. Most of your moves in general won't lead to much of anything; you'll get two-three hit combos in most cases, and trying to overextend beyond this is dangerous. It's also when you're most vulnerable to all the dsmash tactics I talked about in the last part, as she has full access to crouch cancelling, jumping into your dair, ASDI down, etc. Play it safe here, whatever that means to you. There are Falco players out there who play this part of the matchup purely at a distance. They rack up lasers and chip damage, they hit-and-run with shines and space retreating bairs. There's nothing wrong with doing that if that's how you're most comfortable getting that damage. There are other Falcos who attempt to proactively open her up, and focus on making sure their dairs are perfectly spaced and timed to get combo starters, get their couple hits in, and then back off to reset to neutral. That's fine too. Beware trying to play too aggressively though, as the combo extenders you need to get her into the next part of the matchup will require at least one hard read on their timing and intent. Once she's at the point where dair will start knocking her down and you can reliably follow up on a pillar combo (~40-50%), the next part of the matchup begins: Get your opening and combo the mess out of her.
You can absolutely combo Peach from this %, and you need to keep one very, very important thing in mind when doing so: Peach has the option of either trying to disengage and escape, or holding inwards to try to survive. The options she chooses *must* dictate your combo choices. The goal for Falco should be that you want to continue to combo her until the very instant she tries to escape, and at that specific point, you need to hit her with your combo finisher. Smart Peach players will be trying to escape when they're closer to the lower range here (50-70%), because even a strong Fsmash won't kill anywhere but Yoshi's. In these cases, you want to get good at following up on weak hits or DI mixups to continue the combo on escape DI. You can techchase with dairs. You can nairplane/fairplane. You can pillar with uptilts. You can do crazy-ass **** like full hop fast fall laaaaate nair into a followup. You have quite a few options here, but remember that this stage needs to end with her offstage. That means if you choose incorrectly and Peach escapes, but is high above you with a float, you still have the advantage and you're still in this part of the matchup. You've only taken a loss here if she returns to center stage or pushes you to the ledge, at which point you need to basically play the long game just to get her offstage. If you're doing it right, you want to get a solid 60-80% combo in this part, that ends with a combo finisher like shine off the top, fsmash/dsmash, double dip dair, or a strong aerial to send her offstage. If she's not dead but you still have the advantage, you go to the last part of the matchup: keeping the advantage and following through on the edgeguard.
In theory, Falco should be able to rinse repeat edgeguard Peach. Remember a few things: Peach can't ledgedash and her ledge options are to get up, get up attack, tournament winner, roll up, or double jump into an airdodge, float, or drift on stage. Every single one of these options will lose outright to strong bair. Every one of them. Go back and watch PPMD vs Armada at Pound V; Set 1, game 4, on YS. The last ~50s of the game are PPMD literally just bair camping. If your spacing is right, that's the only thing you need to beat Peach at the ledge. Watch that sequence, and repeat it, every time she's at the ledge. If she winds up offstage, you (and she) have other options, but between laser, bair, and dair, you should be able to cover everything she wants to do. This is the turtliest part of the matchup, and the most crucial. If Peach gets center stage again, you're forced to win neutral at least once more to beat her, and this is where trades *strongly* favor her. Note that in this situation, you might want to camp her out until you hit her with 9 or 10 lasers, because after a protracted edgeguard your bair is going to be way too stale to have a chance of killing from center stage. Much of the gameplay between Falco and Peach has changed since the days where PPMD and Armada played each other in grands, but this part of the matchup has hardly changed at all. Watch PPMD in his best sets, and copy what he does in this part of the matchup specifically.
That's pretty much all I've got for you. It's a sick matchup if you learn the rules of it, and once you practice enough that dsmash stops being a thorn in your side, it's super fun imo. If you still have questions about how to deal with certain things, there's a Falcomaster in the discussion thread who can happily provide more insight. Good luck!
