After you pay a visit to the Pokémon Research Lab and teach your Pokémon Rock Smash, you meet Urbain/Taunie and prepare for the Z-A Royale.
Go Outside and talk to Urbain/Taunie
Exit the hotel and talk to Urbain/Taunie. You'll check the map. There is a Battle Zone just south of the hotel. Enter it, and there will be a cutscene. Whenever you need healing, go back to Urbain/Taunie to heal your Pokémon.
Go into the Battle Zone and you will encounter a trainer who has a level 6 Bellsprout.
Farther in, you find Lida, who recommends trying to sneak up on trainers so you can have an advantage in battle. You can crouch and hide behind things, then use your Pokémon to attack theirs first. Lida gives you a Potion, and points out a trainer nearby who has their back turned.
This trainer has a level 6 Bunnelby and a level 6 Fletchling.
Go back the way you came and head northwest to find Naveen, who has advice about earning medals and avoiding higher-ranked trainers. You get a Sitrus Berry.
To the northwest, a trainer has a Weedle.
Defeat three trainers in total. You can use the map to instantly go to places you have visited before, so go to the Pokémon Center nearby. Talk to Urbain/Taunie outside of the Pokémon Center. If you haven't healed up your Pokémon at the Pokémon Center, do so now, and buy any supplies you think you might need.
Then go northeast to the mission destination. Talk to Urbain/Taunie. Then the battle will begin.
Zach the Driver has a level 8 Slowpoke, a level 8 Pidgey, and a level 9 Pikachu. You get 540 Pokédollars for winning.
Go to the Lobby. This begins Main Mission 05: The City in the Shadow of Prism Tower.
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