I finally got to playing all of these and I really enjoyed them all. I ended up getting all of the achievements (and a World Record if I'm not mistaken) from Part 1-Part 5, since when I was playing through that half of the game I had more time on my hands. I had a lot of fun getting them and plan to hopefully go back to getting the rest from part 6-8. Overall each level felt distinct yet a part of a greater, cohesive whole; everything was clearly well thought out, including all of the Big Coin/1-Up placements/bonus rooms/achievements/etc.
Forest Frolic: This felt like an appropriate start to the game and I really enjoyed nabbing the wold record using the secret exit (I might have lost the WR between then and now, I haven't checked in a bit). From the get go it was clear that you had an eye for the standard Mario World aesthetic and "flow", so this got me excited to tackle the rest of your levels.
Peaceful Plains: I really enjoyed getting the speed run achievement here. From figuring out a strategy to flipping that switch block as quickly as possible, to finding various ways to utilize the Cape to shave off time, this felt like a very tightly designed course and utilized the Cape quite well.
Seesaw Spelunking: Another fun and tight level. I appreciated the inclusion of the seesaws as an overall theme and I thought overall they were implemented very well into the design of the level.
Wishing Well: Typically water levels suffer from being, well...water levels. I thought it was quite clever making the player travel down. It kept the pacing up and allowed for some interesting alternate paths and rewarded exploration in fun ways, especially with the fun use of the Spike Cap.
Dour Desert: I also really had fun with refining my path to earn the speed run achievement in this one. You consistently seem to manage to craft fun areas utilizing the cape's flight and glide abilities, and the geyser was a clever and thematic way to give the Cape to the player.
Mysterious Mansion: I enjoyed the structure here and the layout of each room/challenge felt good. It had just enough of a "puzzle feel" to be fitting as a Ghost House level without ever becoming overly frustrating like many Ghost House levels can sometimes be.
Slippery Slopes: I'm always a fan of having alternate paths from time to time. Giving small Mario some fun paths to take advantage of his smaller size should be featured in more levels (I need to do this too). This had the most difficult secret Star for me to get personally, but I don't believe I ended up finding the one in 6 or 8 yet.
Castle of Chaos: You did a great job laying out the tracks for the obstacles/powerups throughout this level, as I had a lot of fun navigating around the various obstacles as I went. But for whatever reason, I was simply unable to position Mario on that one moving platform correctly to get inside the levitating door after that checkpoint. I must have tried 10 times before giving up and moving on. The boss fight was a lot of fun and clearly I can see where one of your other levels got its inspiration from. :P I still need to find the secret boss, though!
I meant to share my feedback way sooner so I could have more things to comment on (as the earlier levels were fresher on my mind a week ago), but I remember these thoughts standing out in my mind after playing through each one. Overall it was an extremely enjoyable time and felt like they each could have been stages pulled straight out of a legit Mario World game, so awesome job!