Based on my limited experience:
Downsmash is really crappy to get hit by. Especially at early percents. Don't go balls-deep with your platform tech chases unless you can hit them very consistently and have a good read on Peach. With that also said, don't change Peach too much with tilts at low percents in fear of downsmash. IMO fair bair grab and needles are by far the best options at low percents. Work on your shield pressure too so you can fair safely and just get away if they try to FC nair you.
Grab is stupidly good for many reasons - Guaranteed kill at X%, does a ton of damage, sends Peach upwards where she's stupidly vulnerable and can't CC downsmash and destroy you. Try to land it as much as possible.
Work on your movement. A lot of it is being pretty sneaky and avoiding Peach's attacks while going for 1 of the 7 things you can do. Even slow changes in pace combined with some wavedash backs is really good. However, do not be cornered by peach. Its asking to get faired. On the other note, try to corner peach. - She doesn't have a good wavedash/roll and you can probably uptilt or fair her float on reaction if she tries to get away there. Same for the other tools. She really sucks when cornered and if you watched the tournament today, You'd see that Armada is forced to ledge stall a lot / fight with float fair to get any breathing room.
There's a bit more things but IMO just focus on these for now. I like fighting Peach on Yoshi's and Stadium for the vertical kills and platforms. FD I usually stay away because it makes Peach's edgehogging even more 'guaranteed' against Sheik.