Battle: Pilot Chase (2160 Poke)
Opponent: Ducklett Lv 36, Swoobat Lv 36

Wait here for the wind to blow so you aren’t tossed anywhere, then head straight up at full speed.  This will bring you to the last and largest shelter, where Skyla waits for you.

Battle: Gym Leader Skyla (4680 Poke, Jet Badge, TM62 Acrobatics)
Opponent: Swoobat Lv 37, Swanna Lv 39 (Sitrus Berry), Skarmory Lv 37
Item: Hyper Potion

Skyla greets you eagerly when you arrive, having waited for this battle.  Her Swoobat is a strong opening with Acrobatics and Heart Stamp, but it’s the Swanna you really need to watch out for- between its Big Pecks ability preventing your reduction of its physical defenses and its use of Bubblebeam and Air Slash, only an Electric pokemon will really be able to handle it well.  Rock-types will be unfortunately flattened by the water bird and Grass-types lose out to the Flying side.  For all that Ducklett isn't too great, Swanna can set itself up to be a pretty solid wall.  Skarmory is considerably less threatening, if only because of its low attack stats, but it takes a considerable effort to lay out the metal bird, so be prepared for a long fight.  Thankfully, by the time you get to it, you've probably done most of the switching you're going to in this battle and its potential to lay in entry hazards ceases to matter so much.

When you beat her, Skyla congratulates and thanks you, claiming it’s been roughly two years since she’s been able to give a battle her all.  She gladly forks over the Jet Badge and TM62, which contains Acrobatics.  Acrobatics is a slightly quirky but powerful Flying attack with a base strength of 55 that doubles to a staggering 110 if the pokemon using it doesn’t have a Hold Item.  This works especially well with the various Gems that get used up by a single attack, but can also be made to work with Berries or, if the pokemon is fast or strong enough, with no Hold Item in the pokemon’s grip to begin with.