In Pokemon Black and White, the third Pokemon Gym you’ll face is the Castelia City Gym which is located on Gym Street.
Burgh is the Gym Leader and he is a specialist of Bug-type Pokemon. The gym is designed like a beehive, with honey walls that you walk through, and regular walls with Burgh’s artwork on them. When you first arrive at the gym Cheren will walk out and tell you that he’s got the Insect Badge. Burgh will then pop out of the gym afterwards and tell you to go to the Prime Pier. When you’ve done the side-quest with Team Plasma head back to the gym.
When you walk in the gym, tall to Clyde to receive a free Fresh Water. Walk through the first honey wall and press the button in the center of that room. After that, go to the left and you’ll be challenged by Harlequin Jack. Defeat him and continue left and then press the other button in the room.
After that, go through the honey wall next to Harlequin Jack and press the button on the center. Harlequin Kerry will pop out of the ground and challenge you. Defeat him and head to the right and press that button. Then head to the left and press that button. The gate to the right of that button will lower, allowing you to pass through the honey wall. Go through that honey wall and press that button.
Exit through the honey wall, and go left. Press the button on the far left. The gate next to that button will then lower, allowing you to pass through the honey wall.
Go through the honey wall to the south of your position, and head left. Press the button and Harlequin Rick will appear and challenge you to a battle. Defeat him and and enter the honey wall above him. Press that button. Another gate will lower. Exit the honey wall behind you and the other honey wall.
Head north, enter the honey wall, and you’ll be challenged by Harlequin Louis. Defeat him and press that button. The final gate will lower, allowing access to the Gym Leader’s room. Exit through the honey wall behind you, and enter the honey wall next to it and get ready to fight the Gym Leader.
Burgh has a lv21 Whirlipede, a lv22 Dwebble, and a lv23 Leavanny. If you have a Flying-type or a Fire-type, once again, you’ll breeze through this gym. Whirlipede likes to use Poison Tail and Pursuit. Dwebble likes to use Smack Down, Struggle Bug, and Faint Attack, while Leavanny likes to use Razor Leaf, String Shot, and Protect. Defeat Burgh and receive the Insect Badge and TM76 which is Struggle Bug.