Here are the steps to catch Shadow Dragonite.
You must catch ALL 82 shadow Pokemon.
Go to Gateon Port
See the lighthouse? Climb it. Miror B. will be at the top. :)
Battle him. After you battle him (I think you only need to battle the Ludicolo's) he will throw out shadow Dragonite.
Snag him. There you go!
Hope This Helped :D