If World 6 is your destination, you can take a shortcut at the very beginning of this section. Pop up the vine and bounce off a Koopa Paratroopa for a boost to the top. First you'll be taken to Coin Heaven B, and when you're done, you'll arrive at the World 6 Warp Zone.
Otherwise, you must find a way to scale the massive wall blocking your progress to the end of the level. Two well placed jumps will reveal hidden Coin Blocks that you can use as stepping stones.
When moving platforms are three circles long (as opposed to the standard four or six), keep in mind that an entire column is one sprite.
The two platforms in one column will always move in uniform. There is only one sequence that will repeat itself.
You will also notice that these platforms are restricted, compared to other platforms. While the objects in the sprite will move, the sprite itself is frozen! Therefore, it cannot go higher than the top of the ceiling - it will just cut off.
To collect a 1-Up, be sure to grab the Starman found at the beginning of this section. Then jump on top of the second pipe, and hit the brick in the high right corner. As soon as you make it appear, run to the right and grab it when it drops.
Jump from the first rising platform and make the vine pop up from the brick. Then ride the platform again, leap over to the vine, and climb to the Warp Zone which leads to World 8.