After conquering the Stow-on-Side Stadium, you’ll be greeted by Sonia—or, more specifically, Sonia’s Yamper—as you leave the Stadium. She’ll talk about the mural in town, but then after a moment, a loud noise can be heard in the direction of where the ruins were, so Sonia goes to check it out and encourages you to do the same.
Head to the west of the Gym, up a bunch of steps until you find Sonia. There’s a hidden Max Revive to the left of Sonia if you didn’t pick that up during your first visit through Stow-on-Side.
Continue climbing up the steps and you’ll find Bede commanding a Copperajah to smash through the mural on the side of the cliff in order to find Wishing Stars to please Chairman Rose.
Approach him and you’ll start yet another fight against him to hopefully stop him in his tracks.
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His Pokémon have gotten a bit tougher from last time and have even evolved since then, but they’re still a bunch of Psychic-types, meaning your Dark-, Ghost-, and Bug-type moves will be your best bet against him. He also has a Super Potion that he may use to heal his Pokémon during the fight.
His Duosion likes to start off the fight by using Reflect to reduce the damage your Physical-based moves do, so watch out for that if that’s your strategy. Other than that, it’s mostly straightforward, so just try to do your best to take down his Pokémon, keeping in mind that they’re a bit tougher than they were in their unevolved forms.
After you beat him, Chairman Rose, Oleana, and some of the Pokémon League Staff will rush up and scold Bede for what he’s done, and then ultimately Rose will make the decision to boot Bede from the Pokémon League challenge and tell him to go back to Hammerlocke.
A bit more dialogue will take place between you and Sonia, but then the mural will collapse, instead revealing some special statues of two Pokémon—one wielding a sword and one wielding a shield—as well as two heroes behind them.
A few questions later, Sonia will finally let you go to continue your Gym Challenge, but not before giving you 2 Revives for free. Nice!
Now that you’ve gotten that taken care of, your next destination is the Glimwood Tangle, which you can access by heading to the east of the Stow-on-Side Stadium.