Notice the arrow platforms rising from the blue lava, and sinking back into it in short order. These temporary bridges are your only way of crossing lava gaps throughout this level.
Ignore the Parabones while crossing this lava gap, they are merely a potentially costly distraction.
Green Star #1
The Green Star Ring has its Coins over the lava, which you can reach by using the arrow platforms.
Arrow platforms, lava, and spiked rollers make for a very dangerous combination. Remember, you can safely stand on top of the central part of the spiked rollers while you plan your next move through this section.
Stamp
The Stamp can be found just off to the side of the main path made by the arrow platforms.
Green Star #2
As with the Stamp, the Mystery Box leading to the second Green Star’s bonus room can be found along the way. In the bonus room, you have to defeat a Bully within 10 game seconds to collect the Green Star.
Beyond the Checkpoint Flag things become a bit easier. Arrow platforms now extend from the nearby walls to help you cross lava pits, Additionally, there are rolling platforms protected by spiked rollers, a dangerous combination that can result in a blue lava bath.
Green Star #3
The last Green Star is next to one of the rolling platforms, in easy reach. Watch out for the spike rollers here!
The last challenge before the Goal Pole is to take down three Bullies. Defeating them causes a bridge to rise from the lava, and triggers a set of arrow platforms that you can use to reach the top of the Goal Pole.