I was able to fly with a cape over most of the level, but it was pretty difficult, as you would hit the edge of the screen if you went too fast and fall. It took a little practice.
But in the end I beat it without a cape. I'm guessing you may be stuck at the part where you are standing on the perch which is moving downward, trying to jump past the turtle onto the first log in the game. I figured out the exact place that the turtle had to be at, and jumped up and down while I waited (to prevent the post I was standing on from going too far down) then took a running leap from the log, or whatever you call it, and hit the turtle on my way to the log. The rest from there isn't too hard.
The trick I learned was to jump up and down, staying in the same place, on those logs that go downward when you step on them (not the bars that drop almost immediately). If you jump up and down a couple times you give the screen enough time to move so you can see where you need to go next. Hope this helps! If not, perhaps you could explain exactly where you are stuck and maybe I can help you (I was just playing this level again today so it's pretty fresh in my mind).

The best way to approach any level is with a cape every time you try it. Though some levels in this game are harder than others, none of them are very difficult in comparison to the eight levels of the star path! If you are really struggling with a level and you have accessed the star road, you can always go get a purple Yoshi and fly over most of the level. I'll have to look up Butterbridge for more helps.

Yes, there are two flying red turtles that you are suppose to bounce off of on this stage. You can probably get away with a poor jump on the first one or use your cape to float onto him. You can always use a Yoshi to pass one of these parts by ditching Yoshi to get a higher/farther jump.