Rematch with Koopa the Quick
From the Super Mario Wiki, the Mario encyclopedia
To reach Koopa the Quick, the player needs to make it to the base of the mountain near the Shrinker Pipe. If on the tiny island, the player needs to take the pipe so they are on the huge island. Going down the hill past the hole out of where the iron balls roll, the player will be in a field with Koopa the Quick waiting on the opposite end. Talking to him will have him ask the player if they are willing to race him again, claiming he has some new "Koopa Mach 1" ("Supa Koopa Sprint" in the DS remake) sneakers to help him win this time, obtained at some point after losing the last race. Like with the last race, Koopa the Quick will offer the challenge only to Mario in the DS version.
Accepting his challenge will start the race, and Koopa the Quick will begin running toward Windswept Valley. In order to reach the valley and beat Koopa the Quick to it, Mario has to run past the iron ball spawn hole, down the ramp and the ledges, and across the bridge with the wind blowing across it, and finally reach the flag in the valley. If Mario beats Koopa the Quick to the flag, he will reward the player with the Power Star. Additionally, using any of the Shrinker Pipes will restart the race.
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