Peach is one of our worst non-high tier match-ups. Her Fair range and spacing via glide can punish most of our aerial approaches and if we're on the ground, she can abuse our fast falling properties to perform a 60%+ combo string.
Example; Dair -> Dair -> Ftilt -> Ftilt -> Utilt.
Dair -> Ftilt -> Jab -> Grab -> Down Throw -> Down Throw -> Ftilt -> Utilt.
There's a lot of stuff she can do to us combo-wise that it's almost impossible to avoid. She can string a chain a down throws on us that can rack up just as much damage as Falco's chaingrab, or more, even, if she follows up with Ftilt -> Utilt afterward.
Try to be patient and campy until you can find an opening. It's possible for her to auto-cancel all her aerials, but if she falls at the wrong time, it leaves about 4-5 frames for you to punish her. Some of her attacks have long hitboxes that *DO* allow her to hit you many frames after it comes out -- such as Dair and Bair. If she uses those against you, spam short hop Nair. I would recommend Uair, but considering most Peach users abuse her glide right around the character's head (where she can safely string attacks), it's hard to get close with a Uair so it hits. You have to be extremely close and have godly buffering for Uair to punish him from that position, so approach with short hop Nairs, fastfall, rinse and repeat.
On the ground, avoid Peach's glidetoss -> Dash Grab. Like I said up top, she can combo a down throw into a ftilt -> utilt or even a pivot jab -> regrab. Sad thing is, Falcon's vulnerable to most of these strings. Not as vulnerable as Snake, but pretty **** close. Her ground game isn't difficult to get around though, so just play safe and try to pressure with ranged attacks.
Also, discussions like this go in the General Discussion Thread, not the Index.