Truth be told, your opponent was not a very good battler. He could have used Aron, then he could have sent out Infernape to beat your Pokemon, but he did the worst thing possible - send in Blissey.
Anyway, see my brother sweeping a team with Mew and beating *Gasps* Tyranitar, Metagross, Terrakion, Hippowdon, Garchomp and Heatran! What is so special about this? Well, 4X Super Effective Focus Blast from Max Special Attack and Choice Specs Gengar is NOT enough to beat Tyranitar, but Mew still beat it! Mew even took THREE Outrages from Garchomp!
http://pokemonshowdown.com/replay/ou-41406432
True. I was thinking, "What? Why switch out of Infernape?" Because Infernape broke your Sub, and you were in the open against a Mach Puncher. Then he switched I was like, "No! Now Swartzentuber will just put up another Sub!" BTW is there a nick name I could call you for short?
And, yeah, Mew is overwhelmed any Status, Volcarona, Scizor, Politoed, and anyone who can use Clear Smog or Leech Seed.