Hahaha, this passerby from Brazil just challenged me, using Mewtwo Y, Yveltal, Zygarde, Garchomp, Blaziken and Lucario. It was my first Link Battle, and I didn't know how to access Pokémon in my box, so I had Tyrantrum, Volcarona, Aegislash, Kangaskhan, a Shellder I'm training, and Yveltal (just did that part of the story).
His Mewtwo Y killed my Tyrantrum really quick, but then my Aegislash killed him off with a combination of King's Shield and Shadow Sneak. I proceeded to take out his Blaziken in the same fashion. His Lucario then killed my Aegislash. My Yveltal took out his Lucario with Oblivion Wing, and then Roosted up when he sent his own Yveltal, which kept using Focus Blast. My Yveltal held on and eventually killed him with Oblivion Wing. I was then in the middle of killing his Garchomp with Oblivion Wing (half his HP gone in one hit, restoring my own in the process) when he quit. Seeing as Zygarde is same type and similar stats, it probably would've ended in defeat for him.
I think his name was Guto. If you see him challenge you, expect him to have a team full of legendaries, lol.