After clearing the second trial, you can receive the third--and final--trial from Mustard in his room in the dojo. Despite all the dramatics your task is simple: defeat Klara/Avery in a no-holds-barred Battle. Once you're geared up for battle, head for the Battle Court, through the back door of the dojo. Then speak to your overly-eager rival to begin.
Pokémon Trainer Klara
At the start of the battle, crafty Klara will toss Toxic Spikes on the floor. These will inflict poison on any grounded Pokémon that switch in. As such, try not to switch unless necessary, or only switch in flying/levitating or poison-resistant Pokémon.
Skorupi is easy--smash it with Fire, Flying, Rock or Psychic-types. If she sends out Galarian Weezing, Steel-types are ideal. Meanwhile, Whirlipede is also weak to Fire, Flying, Rock and Psychic.
Finally, the mystery behind her Galarian Slowpoke is revealed: its evolved form, Slowbro, is both Poison and Psychic! This means it's weak to Ground, Ghost and Dark. Its Quick Draw ability sometimes lets it move first. Also, since it's Klara's last Pokémon, she will Dynamax it.
Pokémon Trainer Avery
Naughty Avery will trigger Psychic Terrain when the battle begins. This terrain boosts the power of Psychic-type moves and protects grounded Pokémon from priority moves such as Quick Attack. It's the Psychic-type boost that should concern you.
Galarian Ponyta should be easy. It's pure Psychic, although it does carry a Fairy-type move. So Dark-types should be mildly cautious, although we doubt it'll survive a hit. Swoobat has the same weaknesses as its unevolved form: Electric, Ice, Rock, Ghost and Dark.
Kadabra is another pure Psychic, but Dark-types can fully relax. Finally, Avery has a Galarian Slowbro like Klara. Again, it's susceptible to Ground, Ghost and Dark. Watch out for Quick Draw, which sometimes lets it go first and expect Avery to Dynamax it in a pinch.
Unless something goes horribly wrong, you should pass the trial with flying colours. The only way you could seriously lose is if you came to the Isle of Armor very early on. In which case, feel free to train your party a bit more. Assuming you've won, everyone will congratulate you. Then you'll be taken back inside the dojo, ready for a chat with ol' Mustard.