Just to pop in and say: An explore run is defined as the 4 explore battles and the mini boss battle (and if this provides enough mythstones to unlock the mythic battle, the mythic battle forms part of the explore run too). The game actually looks for just that mini boss or mythic boss victory so you can have explore runs prepared ready for a new campaign task. Kind of like beating the system.
I agree that not everyone instantly knows what an explore run is so I try to list them on the bottom of my Campaign graphics to help clarify.
I’ll grab the link to the thread, it has lots of tips on that may prove useful