Demon Hunters have the 'turn Vault's cost to Hatred' option when dual wielding the Danetta's Set Xbows.

Wizards have a chance now with the Aether Walker want (a seasonal legendary) that ( mostly) removes the cooldown on Teleport. These conquests can not be done solo, and not even done in parties, without great cooperation and some items that enable spectacular movement speed. and there's a solo DH as well, also on Asia. I talked to some players in-game tonight who were were fairly certain Sprinter/Speed Racer could not be done solo, and yet here we've got a Crusader who did it on Asia. There's one exception the first person to earn Sprinter on Asia, did it solo, and with a Crusader. You see a scattering of other classes, including Crusaders and Wizards and Witch Doctors, but it's almost all Demon Hunters. No more than 11 characters have done it on any of the realms, HC or SC, and almost all are parties of 3 or 4 Demon Hunters. If you refer to the screenshots below for the current handful of completionists, it's a pretty select group. It sounds impossible to many, but if you check the Leaderboards it's already been done, and on all three servers, though only by a few players. That's not an hour per act, as in the regular achievement, but all 5 acts in less than 60 minutes. It's the same achievement for softcore (Sprinter) and hardcore (Speed Racer) beat All Five Acts in story mode in under an hour. There's been a fair amount of discussion in the community about the fast clear of all five acts as a seasonal conquest, and how or if they can be done.

Diablo 3 Season Conquest: Sprinter & Speed Racer

Diablo 3 speed demon conquest