The guy at the front of the gym will give you a Fresh Water as usual. This gym has trainers that specialize in Flying-type Pokemon. Flying Pokemon are weak to Rock, Ice, and Electric attacks. In contrast, avoid using Grass, Fighting, and Bug Pokemon in this gym because they are weak to Flying attacks. The unique feature of this gym is cannons. They will shoot you in whatever way you walk into them. Walk up into the first cannon to be shot off into the air. Walk left into the cannon to the west. Walk down the stairs and east into the same cannon. You will land right by a Worker.
There is a cannon to the northeast. Don't walk into in from the west because it will just send you back to Worker Brady. Walk up into it from the south. Walk into the cannon to the east when you land. This will put you by another Pilot to battle.
Use the cannon near him to go south, the next one to go east, the following one to go north, and the final one to go west to Skyla. You will land right in front of her. Heal your Pokemon and save before the battle. Her Swanna is very fast and its Air Slash attack does a lot of damage. Use Electric attacks on it if possible because they do quadruple damage against Swanna.
Skyla will give you the Jet Badge for defeating her. She will also give you TM 62 Acrobatics, an attack that does double damage against Pokemon that aren't holding items. Skyla mentions seeing Team Plasma near Icirrus City. Walk around the cannon by Skyla and use it to go straight to the front of the gym. N will be outside waiting for you. He will talk to the first Pokemon in your party. It will tell him that you are a good trainer. He talks about finding the Dark and Light Stones to resurrect a legendary Dragon Pokemon. After some more talking, N will leave.
Go to Twist Mountain at the northern end of Route 7.
Items in Mistralton City Gym:
Received from the man at the beginning of the gym.