Okay, I watched the Mute City fight, here it goes...
-Don't start floating and coming in for an aerial from so far away, it gets very predictable very quickly, and that will get you punished. Get close and instant float an aerial, FF it, and go from there. Or at least manipulate the space so that it isn't so obvious. If you get up in the air on the opposite side of the stage and just float towards them, you're practically holding up a sign "90% chance I'm coming down with an aerial."
-Try to cut back on the rolling, you left yourself vulnerable on numerous occassions.
-Peach's WD may be lacking in length compared to other characters, but it is an incredible useful asset for quick spacing and making peach play at a good pace. This will also help you cut down your rolling. Try to implement it.
-You need more turnips for sure. Turnip spam is good.
-You were on Mute City, so edgeguarding should be even easier. Use turnips to drive Shiek where you want her, in this case you only need to make sure she has to use up+b, and you can push her back off with whatever attack you see fit. For general edgeguarding, fair, bair, nair, edgehogs, the aforementioned turnips, dsmash, situational fsmash and situational upsmash are all good.
-Your approach was rather weak and predictable. Again, turnips can be an asset. Watch a few pro peach vids and you'll start getting ideas.
-Try to be more unpredictable.
-I think you should make use of your grabs more.
Hope that helps you!