At the start, grab the fire flower from the right brick. The next platform also has two bricks, of which the right one can become a gold brick. Soon, you will see a gold ring. By going through the ring, you can send the koopa below flying back and forth across the platform to get lots of coins. Alternatively, you can activate the ring and run right to safely get the first star coin from the Hammer Bro. If you don't make it in time, just attack the Hammer Bro by jumping from below.
At the midpoint flag, the block on the right contains another fire flower. Soon, you'll see a Red Ring, which requires you to avoid a Boomerang Bro. Whether you decide to risk it is up to you, but if you take the bait, you'll have to return to where you began anyway. There, drop down, and you'll discover a yellow pipe. Inside are two Boomerang Bros guarding the second star coin. You can either dispatch of them from a distance with fireballs, or carefully weave your way down there to get the coin.
When you exit the chamber, jump up to reveal hidden blocks, which can be used to get back up. Continue going right until you see an arrow pointing up. From here, you will have to ascend via the elevator while dodging hammers from the nearby Bro. On the next level is a Boomerang Bro, which can be either ignored or dispatched of using the nearby koopa or by jumping from below. On the top level is a Sledge Bro, which throws massive hammers. You can defeat it using the fire flower in the ? block to the right. Go to the left to discover a new platform containing a Paragoomba and the last Star Coin. Then, head back right over the short barrier. There will be nothing else between you and the flagpole.