Instructions
Surf south from Pallet Town onto Route 21. Battle all the fishermen on the route until you defeat Fisherman Gideon. This will register Mantine̵7;s identity in your Pokedex.
Fly to Goldenrod City and enter the Global Trade Station. Talk to the receptionist and enter the trade area.
Offer to trade one of your Pokemon for a level 10 or higher Mantine. Exit the trade area.
Reenter the trade area every few hours. You will likely receive a Mantine within one day.