Yes, Pokemon with hidden abilities can be used in wifi battles. Azumarill has the hidden ability Sap Sipper, which can be caught in-game at the floccesy ranch hidden grotto as a marill. It is shiny either because of catching it shiny(which I doubt because of the very small chance of finding a shiny Pokemon combined with the chance of finding a marill in the grotto), breeding, or of course, hacking. There is always a chance of it being hacked, but the ability is totally legit. I hope this helps! -Jellohamster
