After you achieve the rank of First Star in the Survey Corps, you learn of a request from Mai of the Diamond Clan.
Meet Rei or Akari at the Training Grounds
Go to the guidance marker (you can quickly travel there by selecting the blue wing symbol on the map) to reach the training grounds. Talk to Rei or Akari, and after a cutscene, you will do battle.
Rei or Akari will send out a level 9 Pikachu.
After the battle, you will meet Zisu, who teaches you about Strong Style moves and Agile Style moves. Strong Style moves do more damage, but your pokémon won't be able to act as quickly afterward. Agile Style moves do less damage, but allow your pokémon to act again sooner. Both Strong Style moves and Agile Style moves use more PP. Zisu can also teach your pokémon more moves if you talk to her later. She will be at the Training Grounds.
Communications
You can now go into your Satchel and press ZR or ZL to go to the Communications section. You can turn on the Internet connection here, and can choose whether or not to automatically connect. If you connect, you will need to save your game.
Lost & Found
The communications section includes the Lost & Found, where you will find the lost satchels of other players. Returning them will reward you with Merit Points, which you can spend in Jubilife Village for items. Look for lost satchels in the map. If you have a subscription to Nintendo Switch Online, other players can find your lost satchels if you collapse in the wild, and send the items back to you.
Mystery Gift
The Mystery Gift section allows you to receive special gifts from the Internet or with Codes/Passwords.
Go to Obsidian Fieldlands
Use the map to travel quickly to the Front Gate by selecting the blue wing symbol there, or by pressing X and choosing Front Gate as the destination, then talk to Ress and ask to go to the Obsidian Fieldlands.
There will be a cutscene, where you will learn about the Back Strike technique. Hit a wild pokémon from behind to improve your chance of catching it or to start battles with an advantage.
Meet Mai
Go toward the guidance marker, and you will reach a bridge. You need to talk to the Galaxy Member before you are allowed to pass.
Then go to the guidance marker, and there will be a cutscene, and Mai will challenge you to battle against her level 10 Munchlax.
Afterward, Mai will heal your pokémon, and will give you 5 Vivichokes. You will learn about the alpha pokémon at Deertrack Heights.
Battle the Alpha Pokémon
Make your way to the guidance marker, where you will find Mai. There will be a cutscene. Mai will heal your pokémon. When you are ready, approach the alpha pokémon to do battle.
After the battle, Mai will heal your pokémon, and there will be a cutscene. This completes the mission. Afterward, the Heights Camp will be set up here, and you can travel directly to it from the village, and directly to the village from it. If you completed any research tasks, you will get paid and receive points now. Then there will be a cutscene, and you will be Summoned by Commander Kamado.