Sheik, Fox, Marth and the Links are Peach's hardest matchups respectively.
Smart Sheiks will not have many opening for Peach to capitalize on and will have good spacing with tilts, camping with needles to build up damage, grabs if you make one mistake, Needle cancel -> grab combos and Fair Shield Stun traps on Peach. Peach CAN NOT afford to shield often in this matchup or Sheik will continue to make constant pokes at her. It's still a winnable matchup (4-5 IMO); however, it's important to take an aggressive stance and forcing Sheik to stay on the defensive. Try using FC aerials to get behind her and quickly turn around then grab. Of course, use turnips to slow her down.
Azen does well in the Peach vs Sheik matchups though. He has a stylish movement which allow him to continously stay on the aggressive. I think Azen perform several WDs out of DJ Lands to assist with his attack accuracy. Any ideas on what he's doing? I remember seeing a matchup vs him and Doll at Chudat's biweekly. I'm not sure if it's still up though. If Peach players were able to master Azen Peach movement, I think that Peach would be much closer to top tier because they would be continuously on the offense and would put more pressure on opponent much like Fox's primary strategy.