Instructions
Stop at the Pokemon Center next to the gym and gather Pokemon with high strength, ice and water attacks. If you've captured and leveled them (to around Level 40), Lapras and Jynx would be ideal.
Enter the gym. You'll immediately be challenged by a trainer that is easier to defeat with your strength Pokemon.
Go upstairs. You will encounter three sets of boulders. Push all of the boulders into the holes except the top right boulder. Defeat the two trainers using you strength Pokemon again. You will encounter Claire, the gym leader.
Use a combination of ice, water and strength attacks to defeat Dragonair and Kingdra.