I find this matchup particularly frustrating because you have to just be patient and avoid situations where you can't respond with much, such as shield pressure and jabs. Just use spaced Backairs and be careful when pulling a turnip because of the amount of vulnerability.
One of the biggest mistakes I made with this matchup is assuming Captain Falcon is an easy character to edge guard. I mean, Falcon's recovery is pretty bad, but it's quite common for Falcon players to recover high onto platforms (Obviously depending on the stage). Sounds dumb at first but it's actually effective for a Falcon player, at least in this matchup, and is something you really should look out for. The simple reason being is that Peach's vertical mobility is slow, which means Peach will take longer to reach the higher platforms. This crew battle at Heir II is a good example, if you skip to 11 minutes into the video you'll see Armada's Peach vs Fuzzyness' Falcon, Fuzzy actually playing the matchup really well. In that one game you will see Fuzzy using high recoveries to his advantage. There were times where Armada simply didn't make it to the top platform in time, and at times Fuzzy had enough time to block anything Armada threw at him after landing on the platform. This is just a thing I think it's important to look out for