After you challenge Koopa the Quick, run up the bridge as usual. However, when you get past the bridge, run over to the flower patch near the red block. If you go to around the middle of it, you should teleport directly in front of the mountain. From there, instead of going to where the rolling bowling balls are found, go up the steep hill. This may not seem it is faster, but it is. Continue running up the mountain until you reach the first hole where the bowling balls are coming from. Jump into the hole. You should be teleported to the second bowling ball hole. Then, run up to the flag. If done correctly, this should be an unbeatable strategy for defeating Koopa the Quick.