The gaps in the floor move back and forth. As such, you should not try to run right in them and jump over the gaps as you see them.
Halfway through, a Fishin' Boo will pursue you. Its flame is lethal, and its presence really restricts your ability to jump, making it difficult to avoid incoming threats.
You can get a feather from the ? block if you wish.
At the end, you can obviously only enter the door if it's not suspended in mid-air. Once solid ground comes back, enter it to get to the second area.
This area contains several new enemies. The Boos move diagonally and bounce off walls just like the fireballs that appear in castles.
The Boo blocks are more interesting: if you turn their back they pursue you, but if you look towards them they become blocks that are perfectly safe to stand on.
The flower in the ? block is a bit difficult to collect and best avoided. You can, however, go to the very end of the area and grab the 1-up mushroom from the turn block if you wish.
Ultimately, you will want to reach the door at the top. To do so, you must lure the Boo blocks towards you so they form a staircase that allows you to reach the door. A different, but harder way is to spin jump off the Boos in the area.
Once you have reached the door, you're done; the door leads to the goal tape.
