Kenny White rushed to the gates of Walt Disney World’s Hollywood Studios in Florida at 5:30 a.m. on a recent Wednesday to be among the first in line to hop on Slinky Dog Dash.

Even the slightest delay could spoil the 50-year-old’s chance to finish the Parkeology Challenge, a marathon-like endeavor to take a spin on all 49 rides in the Orlando, Fla., resort’s four parks in a single day. Slinky Dog Dash, a popular new coaster attracting big crowds, would be his first major hurdle.

“Every minute matters; you give it one minute on one attraction and everything kind of cascades,” says Mr. White.

For an elite group of Disney superfans, doing it all in one day requires months of planning. Challengers dart from the Mad Tea Party to Space Mountain while braving the Florida heat, swarms of tourists and the occasional broken toe. Runners map out detailed routes in hopes of joining the few dozen who have ever completed the grueling race. To endure the 20-plus-mile day, some train by hitting the treadmill, Rollerblading or running in quarter-mile sprints to imitate racing between rides.

There is no grand prize, only celebrity status among other admiring fans.