The Sprinter/Speed Racer Conquest description can be confusing. (What was Blizzard thinking? — Oh… yeah…) The description just says to complete Acts I through V in 1 hour. And since Seasons have to be completed in Adventure Mode, who would think any different?
If you want to try it, make sure you change your Game Settings to Campaign Mode → Act I, The Fallen Star and set the Game Difficulty to Normal. (To make it easier). The timer starts as soon as you click START GAME .
That’s what I did. 
Just in case you want to watch someone do the Sprinter Conquest:
