For Yoshi, you definitely want to pick your spots. A lot of what he does is safe, and you have to rely on baiting out his moves in order to do much since his nair hits on frame 3. Approach on the ground, pull turnips when he's really far away/recovering, and based on what he does you can get grabs off shielding his aerials or outpoke him with a bair. When you hit him, get what guaranteed follow-ups that you can, and then get back out before he retaliates with his aerials. It'll be a long battle of attrition, but play safe and patient and you'll have a greater chance of success.
Pikachu and Sonic are both weird in that if they don't want to get hit, they won't get hit. However, once you get a significant lead on them, you can start making them come to you, where Peach thrives. Throwing out nairs and bairs for Pikachu's Quick Attack/Sonic's various spindash approaches will commonly beat them out and hit, though in Sonic's case shield is also a really good option. Just don't try to force the KO too much! They have really quick attacks that either put Peach in a bad situation or lead into kill options, so try to mix in your KO attempts in the middle of quick pokes and shield options to keep them guessing as to when you're going for the stock. Especially against Sonic, don't rely on anything remotely laggy, because that's playing into his superior speed!
For projectile spammers, you REALLY need to be patient and use float mix-ups to the best of your ability. Link has surprisingly fast tilts, so the best thing to do is weave in, hit the ground, and then try to pop him into the air, where he's a bit easier to punish. Dair won't be helping you much unless you're reading a recovery onto the ground. Toon Link is like Link, but with the ability to cover more angles at the cost of weight and KO power(though he still is no slouch in that category!). Just be aware of that, and that both of them can boost their recovery via holding a bomb, and you'll be able to deal with their walls. I can't help on DHD, since I've yet to face one, but I imagine the same is true, outside of any attack using the duck(aerials) are surprisingly lethal, so be careful! At least their recovery is easier to punish.
Mega Man is one of the characters that can give Peach trouble. If you can grab his metal blade, do so, as it's one less way he can poke at you. His best killing move is bair, so if you see his back to you expect the move and respect it. His fair(the flaming sword) will outpoke you, though, so you definitely need to pay attention to what way he's facing. Pellets/lemons are annoying, but they barely do any damage, so don't fret. Peach builds damage really quickly, and as soon as she gets an opening through turnip/metal blade/stabbing at him while he's landing, he can really struggle. Ironically, sometimes the best thing to do with him is to get a significant lead and then forcing him to approach, since his kit is more built toward walling out than getting in. Just like the other walling characters, you NEED to be patient, and with Mega's weight, he could be surviving for a long time. Don't panic, keep calm, and stay patient, no matter if you're in the lead or behind.