I suppose I need to add some stuff.
Don't play too roll or dsmash happy. You need to use more float cancels and space those attacks and camp with turnips well especially against link, platforms help here a lot. Peach has lots of priority on her attacks, so quick float cancel on the right places will make your opponent unable to get to you. It will also help you build up damage more, as opposed to dsmash and dash attack there and there. Float cancels also lead into combos, so use em.
Don't end your combos too early. The first dash attack was perfect setup for uair and after that even more uairs into nair. Link is so easy to combo, so don't go for nair on such low%.
Do not dsmash empty space, dsmash is a quick move but takes a while when she whirls her dress, so you'll be vulnerable to assaults.
You need to up your reaction speed to stuff, many times I just saw you standing there doing nothing and getting hit while you weren't in stun. Even mashing buttons is ten times better than doing nothing on such situation (like mash a for nair, shield is real good too).
Di opposite way where an attack sends you, ie. if attack would kill you horizonal, you can survive by di'ing up and against that attack. While if it kills vertical , di horizonal. Aim for the corners of the stages when survival di'ing. Anti-combo di is either trying to di down and away at low% so you can touch ground earlier and shield/cc, or di up and away so you can get as much distance between your opponent as possible. They wary between situations though, I've seen peach di up and against marth's fairs to mess their spacing so peach gains altitude and won't be in so much stun, so she can get a nair in between or at least when marth bairs and then it's not a tip. There should be doraki's di guide on melee discussion.
Don't taunt till you are certain they are dead, otherwise they just might come back as seen here.
Shieldgrabbing always is bad, try other maneuvers like fc, nair and wavedash from shield.
You also make some random and not always so good choices there and there, pay more attention to what your opponent does and do what is the best option and not a random attack that might possibly have a good outcome. Do what's guaranteed to have a good outcome or has the best chance of success if you play your cards right.
You also need to work some on your edgeguard, like turnip link from above or edgehog him when he hookshot sweetspots, ledgehog makes him not sweetspot, then you can punish him if you just rise up. It's better to save the turnip to when he's either too far away to hookshot or he just did it, making him lose the hookshot. Dair against non sweetspot is too good, other aerials as well. Beware of his ledgehopped aerial afterwards if he manages to grab the ledge. One way to own him would be float backwards to the ledge and z-drop a turnip on him, then edgehog and maneuver yourself accordingly as he comes back, or after that just drop on him quickly with a bair. Against link one aerial is usually enough to maul him if he's too far to use hookshot or has used it already, so don't be afraid to float there and bair him or hog the ledge and drop down bair.
You also need to follow up much quicker and not just stand there and let people recover. And if there is an opening (as in, they lag), use it efficently and punish them.
As said above, you need to use more fc and it would be better to start using some fc in place of dash attack. Good player will start shielding you on 1-2 stock if you just do that maneuver and if you were to roll behind them instead, you'd get mauled with OoS bair (out of shield) instead. Dash attack is quite unsafe approach, so lay off it and use fc on it's place. FC's are also good way to build up your timing and technicality and fastening your peach in general.
Start anticipating where you opponent is likely to go and move accordingly. It is crucial on high level of play to predict your opponent and play smart.
I also dunno if this is correct, but you don't seem to use c-stick for throwing turnips, at least not when grounded. Begin do so asap. You get more boost on the throw and knockback overall and it travels further. On ground, you simply need to crouch cancel and then use the c-stick to smash throw the turnip to desired direction. For normal standing throw, you need to jump cancel it with x/y + z.
You also seem to suffer from beginners fear of getting attacked, thus leading you to roll and sidestep moreso than needed. I've seen this done too many times on my career and good players will always punish you from doing so, even if roll spamming can work to some extend and it's annoying (least not brawl lol), it means you do not punish their actions enough, leaving them with too little damage and then you cannot simply ko em fast enough compared to how fast they ko you. So what you need to do is less shield, roll and sidestep. Start using more evasive maneuvers like dash dance and wavedash (if you want with peach). You do not always need to shield when you see opponent approaching if you can block it with your own attack or just evade it. Shield is better than sidestep and roll in general, you can powershield and quickly punish and shield has many OoS actions you can make as opposed to other dodge maneuvers. They all have their time and place though, shield is good against attacks in general, especially attacks that hit your shield with only one attack, dealing hitstun and then you're free to attack while they're landing. Sidestep on the other hand is good against one action that might be laggy and does not have lingering hitbox (like grab and marth fsmash for example) and roll is good if you need to get the hell away or cannot decide whether something is safe or not and need space.
But always remember to punish if there is chance for it, do not hesistate to move in if you're close enough to punish them. You will in time learn when to move in and when not to move in from experience, but in order for you to learn how laggy some move is and how fast they can recover from maneuver and when it's safe to move in/out, you need to start punishing them.
Hm that came out longer than expected lol, guess I just had lot to say from watchign your vids.
Also nair out of shield, Shield grabs are a bad habit
