You don't need a qualifying race, but it's highly recommended to have some experience in mountainous ultramarathons or multi-day races to manage the long effort.
Yep, well, not much point in just repeating what everyone else said, but damn... that looked pretty hard! Oh, the sequence seems to be mixed up, you have on Tuesday a point where a note that says you've done on Tuesday 105 miles, but then on 'Wednesday' you're back to 93 miles?