The faster way is to get to Mythic fight, and if it’s not the one you want - all kingdoms at time of writing are 1 or 2 Mythics, restart the game. On mobile phones, swipe and kill it, then relaunch it. You get another random pick at the mythic.
FYI it seems your mythstones are consumed when you click/tap on the Mythic Boss battle, but if you back out, you get the 100 mythstones back unused.