I've heard that you can meet special trainers like Cynthia and Wally in Super Battles, but I don't know how to enter Super Battles... I went to the Battle Tree and it didn't give me the option to enter a Super Battle, so how do I enter?
As always, there's the Standard Battle Tree battles, but when you hit a streak of 20, you unlock the Super Battles with tougher trainers and even appearances from Dexio, Sina, Wally, Grimsley, Colress & Cynthia who you will encounter every 10 battles.
So Super Battles occur every 20 battles, but you are still able to encounter a special character every 10 battles.
Hope I helped. :) Source