Up until now, Hammer Brothers would stay in one place. Now they advance forward, and they can also jump directly to the ground from the very top! Your time to bump them off of the floor above you is limited now, so move quickly!
Bounce off the backs of the Koopa Paratroopa pair and leap to the top of the very high pipe. This portal will lead you to a chain of three bonus areas, coin room F, followed by a long windy stretch illustrated in part D below, and then finally to coin room E before rising back out of the first pipe in part C.
If you take the ground route instead, stomp the wandering Koopa in this areas as soon as possible. Then wait for the Hammer Bros. to drop to the ground and send the shell sailing.
There's an invisible block with a 1 up in it, not depicted in the image above. It's at the end of the series of bricks where the hammer brothers are.
Much like World 5-3, this level repeats at the platform until you make enter the pipe in the air. Bounce off the Koopas and climb.
Before you progress, you will be treated to coin room D. Therefore, you won't need to repeat Part A at all.
Getting the mushroom in this area is worth it if you are small: you can then get the hidden fire flower in coin room D and start Part B with fire power. Note that if you die anywhere in this level, you will restart from the beginning of the level, allowing you to always have fire power for Part B, which makes killing the Lakitus and spinies much easier.
It's important that you knock the Lakitu out of the sky before you jump to the on-block Fire-Bar platforms in this area. Negotiating the flames will be challenging enough without a mid-air menace.
Want to try and use sprite limits to your advantage? If so, keep the Lakitu in the air. Let the Spinies accumulate and you could make one or possibly both of the Fire-Bars in the beginning disappear! Quite a gamble, but it could help beginners.
There's no need to dash in this section. Leap with accuracy.
The wind stops at the platform before the final fire-bar in this area. Your jumps will be much shorter, so you might need to dash to land on the final platform.
This section is actually really easy if you're good at long jumps. Just run along the platform with the coins to get up to full speed then jump from one upper platform to the next, never slowing down. You will make it safely to the flag in one fell swoop and won't have to worry about the fire bars or the flying koopa.
If you take this short set of stairs one step at a time, you may get burned. Jump to the top in one big leap and keep moving to the next challenge.
All five of the lifts, some at the end of this section and others at the start of the next, move downward. Jump from the hidden Power-Up Block and aim high. Then continue to cross the gap, making sure that you don't hit bottom.
If you are super-sized, you may need to wait at the final lift until it comes close to the bottom. You can also jump to the very top, then jump and land backwards.