How do you "ride the neon dragon"?
According to the wiki:
After around 1870 meters, The Neon Dragon will disappear from the background, emerging from the terrain after a few seconds. The player is able to ride on his back, which earns the achievement "Neon King".
Also note that the neon dragon's back is made out of square colored segments, and each segment will change color when your vehicle touches it. You'll need to ride on every square of the dragon to get the achievement--merely getting on it briefly won't do. If the dragon's color is entirely changed, you've done it.
Here is a video, set to the time when the person gets on the dragon's back: