Instructions
Select the Fly ability from your trainer's menu and fly to the Fight Area. When you first arrive you will encounter Flint and Volkner of the Elite Four and have to battle both simultaneously. Select your best Pokemon and utilize their strongest special moves to take down these two trainers.
Walk to the northwest part of the area after your Pokemon battle with Flint and Volkner. Talk to the fisherman in this part of town to receive a Super Rod.
Travel to Mt. Coronet using your preferred travel method and make your way to the fourth floor. You will encounter several wild Pokemon, however at this point you should be able to easily defeat them.
Stand next to the waterfall on the fourth floor area and use the Super Rod to fish for wild Pokemon. You have a 30 percent chance of encountering Dratini, so keep fishing until you have an encounter.
Weaken Dratini using your strongest Pokemon. When Dratini's health points are low, use a PokeBall to capture it.