The Fighting Crew Base can be found in North Province (Area Two).
Defeat the Guard at Caph Squad's Base
You will battle Carmen of Team Star, who has a level 54 Croagunk and a level 55 Primeape. You get 2860 Pokédollars for winning.
Enter Caph Squad's Base
If you have defeated the other four bosses of Team Star already, be aware that after you defeat the fifth boss of Team Star, the Academy entrance will be blocked by a Pokémon trainer with high level pokémon.
When you're ready, go to the door of the base and ring the bell. However, you can only bring the first three Pokémon in your party.
About the Star Barrage
Team Star's fighting style is called the Star Barrage. You need to press R to send out multiple Pokémon at a time. You can go back to Clive to heal up your Pokémon. You can also use vending machines to help recover your Pokémons' HP, if you find one. You need to defeat 30 of Team Star's Pokémon within 10 minutes to make Team Star's boss come out to battle you. If you need to exit the challenge early, press Y.
During the countdown, move through the base and approach Team Star Grunts to make them send out their Pokémon. Face the enemy Pokémon and press R to send out your Pokémon against them. Your Pokémon will automatically battle them. They will do better if their type is supereffective against the enemy Pokémon's type. You can press ZR to recall your Pokémon back to you if needed.
Defeat Eri, Boss of Team Star's Fighting Crew
After your Pokémon defeat 30 of the enemy's Pokémon, Eri will challenge you to a regular battle, where you can use the six Pokémon in your party.
Eri has a level 55 Toxicroak, a level 55 Passimian, a level 55 Lucario, a level 56 Annihilape, and a level 56 Fighting-type Revavroom (the Caph Starmobile).
Afterward, there will be a cutscene where you learn more about Team Star.
You get Team Star's Fighting Crew Badge, and TM167 Close Combat. (Press A if nothing is happening.) You'll also get some LP, and more TMs will be unlocked in the TM Machine. You will also receive Pokémon materials that you can use to make TMs.
Explore the Base
After this, you can freely explore the Fighting Crew Base, where you will find various items, such as a Fighting Tera Shard, TM126 Thunderbolt, and a TM043 Fling.
If you want to play the Star Barrage again, you can ring the bell at the front gate of the base.