Let's say I have Machop active with a Focus Sash attached, and my opponent's Mewtwo-EX uses "X Ball" for 360 damage with four Double Colorless Energy and a Muscle Band attached. The Focus Sash leaves Machop with 10 HP remaining. If I then use Ninja Boy to switch Machop with Pidgeot-EX and then use its "Mirror Move" attack, does Pidgeot-EX do 360 damage in return?

Yes, it would. When using Ninja Boy the amount of damage done last turn is remembered by the new Pokemon, so Mirror Move would do 360 damage to your opponent's Active Pokemon.

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