Healing
You probably know that the red poles can throw you long distances, but did you know they can heal you? Use the airwalk technique to position yourself over one of the poles, then drop straight down onto it. Each time you do this you will gain a half of your heart back and one of the segments on the pole will turn white.
Skip Second Boss
Here's how to bypass the second round boss. As you approach the last fall before the second boss, float to the ledge on your left, then jump from ledge to ledge until you see the sign that says you've cleared the round. Be careful, though; you must get the special item before you leave the level. If you fail to do this, you will have to go back to the level and find the item, plus you will run into the second round boss!