Fire Bros. will throw their fireballs into Clear Pipes in hopes of hitting you while you travel through them. You toss your own fireballs into the pipes to counter them. It is faster to simply cross the lava by running on top of the pipes.
Green Star #1
The first Green Star is inside an H-shaped Clear Pipe. Watch out for the Fire Bro on the other side of the blue lava pit, he’ll try to stop you from collecting the star.
Stamp
You eventually come across a set of Fire Bars rotating around ? Blocks. One of these is near a Goomba Tower with a Fire Bro on top of them. Ground pound this ? Block to create a tower that launches you up to the Stamp.
The ? Block tower gives you easy access to the Fire Bro at the top of the Goomba Tower. You must defeat him to make the Warp Box leading to the next area appear.
Just past the Checkpoint Flag is a series of gaps bridged by Clear Pipes, with Thwomps guarding them. You can use the Thwomps or a pair of invisible ? Blocks to climb the wall. Once up top, head to the left to find a pipe. There’s also a + Clock on top of another section of wall nearby, so nab it.
Green Star #2
The bonus room beyond the pipe can be tough to work out the first time. Hit the P Switch to cause a ball to fall onto the track, then jump to manipulate the Red-Blue Panels and help guide the ball to the goal. The second Green Star is your reward.
You could just dive into the Clear Pipes, but there are safer ways to deal with the Fire Bro protecting them. One is to jump over the lava from the top of the wall, using a long jump or a Tanooki Power-Up to clear the gap. The other is to time throwing your own fireballs into the pipes to catch the Fire Bro off guard.
Green Star #3
The Green Star Ring places Green Coins around platforms guarded by Blocksteppers. You can quickly clear them out by setting off the Red POW Blocks next to them.
Two Goomba Towers, with a Fire Bro jumping between them represent the last major obstacle between you and reaching the Goal Pole zone. Having a Tanooki Power-Up or Fire Flower handy is a huge help, otherwise you’ll have to whittle the Goomba Towers down with jumps until you can reach the Fire Bro safely.