(Reposted here since I accidently put this in the main BOTW forum)

Beat the game without using any stamina. If the stamina wheel appears during gameplay, reload the previous save.

For reference, these are actions that use stamina:

Running
Climbing
Gliding
Swimming
Charging an attack (including using a fast spin attack)
Entering bullet time mid-air
Taming a horse
Mounting a Lynel
Pushing heavy objects

These restrictions remove the possibility of using windbombs, BTBs, and other glitches, so it would be significantly different than a regular Any% run. In addition, both leaving the Shrine of Resurrection and getting the final hit on Dark Beast Ganon require workarounds that you really wouldn't see in any other runs.