Before the run begins, you need to align your character up to the left-side railing in order to be able to immediately jump onto it. The official starting point is a few in game feet away from the railing.

When starting the timer, you want to jump up the left-side railing of the spiral staircase. Attempting to jump to cut corners while traversing the railing is risky, but will cut your time significantly. You want to perform the jump on the 2nd block from the corner of each flight of stairs. Always keep moving while climbing towards to top! Stop your timer once you touch the yellow square at the top of the stairs. If you happen to fall off of the railing and onto the stairs, immediately jump back up onto the railing.

After a while, you'll eventually become used to the rhythm of jumping and turning while climbing the stairs. Having a good rhythm is key to achieving the best time possible. After a Rocky-style stair climbing training montage, you could even reach #1!

Good luck with the run!