This little cave area is known as Inlet Grotto and you’ll need to follow the mysterious Pokémon along throughout the cave. It sometimes moves a bit slowly, meaning you’ll have to wait for it to proceed, but you can also look around the cave after you get into its more open areas.
There are a few wild Pokémon you can battle there, as well as some items if you search around, but follow the Pokémon through to the end of the cave and you’ll have a little scene with several Houndour attacking you, then a Houndoom that will battle you, but don’t worry, the mysterious Pokémon will step in before it’s able to attack you and then it will lead you out of the cave.
You’ll be reunited with Nemona, at the top of the cave, and the mysterious Pokémon will lose its strength afterwards. Nemona will give you TM032 Swift, a Special-based Normal-type move that has perfect accuracy. In Scarlet & Violet, TMs are single-use, so you can’t teach them to your Pokémon an unlimited number of times—however, you’ll be able to craft TMs you’ve obtained or unlocked using materials you can earn from fighting specific Pokémon, so don’t worry too much about using anything, as it’s usually not a problem to get another, especially towards the end of the game.
Poco Path Lighthouse
Keep going to the lighthouse and you’ll run into a guy named Arven looking into a window. He recognizes the Pokémon, while Nemona recognizes his mom (in Scarlet) or his dad (in Violet), who is a famous professor. Arven will explain that the Pokémon’s name is Koraidon (Scarlet) or Miraidon (Violet), and will then challenge you to a battle after some more dialogue.
300
Tackle-
Tail Whip
Bite
He uses a Skwovet Lv. 5, which shouldn’t be a problem to take down, as it’s a pretty weak Normal-type. You can always use your starter Pokémon, but you might be able to take it down with something else.
After beating him, he’ll give you Koraidon’s Poké Ball (Scarlet) or Miraidon’s Poké Ball (Violet), although you won’t be able to use the Pokémon for quite awhile, don’t worry. It will just sit in your inventory until you’ve finished going through the “prologue” of the Academy.
Climb to the top of the lighthouse by going up the ladder, and then talk to Nemona. She’ll point out the Academy off in the distance, plus you can see quite a lot of surrounding area from up here.