Run To The Demon Door And Back:

The character does not run by default. You must press the B button to run. Before you talk to the character that starts the race, be sure you are facing in the direction you need to run. When the timer begins immediately start running and be sure to avoid everyone in your path. Run straight around to where the door is and line yourself up directly down the middle of the rock bridge. As soon as you touch the door (you don't have to select it) push the stick in the opposite direction and you should go straight back across. Then just avoid all people on the way back and as soon as you see the dialog balloon (aiming at the race guy) hit the button to end the challenge.