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Mewtwo? Most powerful Pokemon? HAH. I killed a level 72 Mewtwo with a level 1 Rattata.
You're going back into the D/P 4th gen, where it's possible to have a Level 1 Pokemon (through Breeding). As such, you bred your Rattata to start with Endeavor and Quick Attack, and made it hold a Focus Band. There are two main ways to out said Rattata without losing at least one of your Pokemon to it: having an Extremespeed Pokemon, or making their Focus Band useless.
Also, I would imagine that the Level 1 Endeavor Rattata is broken in the way people in the past have complained about Double Team (all gens) and Wobbuffet (3rd gen and beyond). (Although I completely understand where they're going with Wobby, since it's immune to just about everything except Toxic or another reliable move that inflicts Sleep, Burn, or Poison, but doesn't inflict direct damage.)
And, to cap it off, the guy who kept his Mewtwo in play against that Endeavor Rattata is an idiot.
It's not who you are underneath. It's what you do that defines you.
As such, you bred your Rattata to start with Endeavor and Quick Attack, and made it hold a Focus Band. There are two main ways to out said Rattata without losing at least one of your Pokemon to it: having an Extremespeed Pokemon, or making their Focus Band useless.
First, it's a Focus Sash, second, there are so many ways to make the Focus Sash useless that makes the strategy not broken or comparable to Double Team and Wobbuffet, at all.
I usually keep a Beedrill on my team through Rock Tunnel (useful for that pesky Kadabra of Gary's, and it tears through Erika's gym like no other). Pikachu I'll catch, then toss for Jolteon. I'll pick up an Abra the instant I've crossed Nugget Bridge, volve it, and then trade-tradeback for a lvl 16 Alakazam. Lapras is a must-have. I don't like using the legendaries.
When building my final team I aim for maximum type-matching threat range per pokemon. My Nidoking, for instance, can cover eleven types at once (twelve in the RBY world where the only ghost is also poisonous), inlcuding all of his non-Psychic weaknesses.