Professor Laventon will give you this mission. (left), For this mission, you'll be working on the Pokédex. (right)
Mission 4 will be given to you by Professor Laventon immediately after completing Mission 3. Your task is to return to the Obsidian Fieldlands, which you briefly visited during Mission 2, and work on improving your Pokédex, which Laventon just gave you.
The people of Jubilife Village need you to solve their Pokémon-related problems. (left), It's a good idea to accept requests as soon as you see them. Many requests you'll naturally fulfill by playing the game. (right)
Initially, you’ll walk along with the Professor and Akari/Rei. Noticing you’re heading out, one of the guardsmen standing outside Galaxy Hall will catch your attention. This fellow, Beauregard wants a favor from you.
Continue ahead, near where you captured the Starly. Towards the left, Akari/Rei is waiting with more nuggets of advice. He/she will encourage you try doing some Research Tasks for Starly, since you’re here.
Akari/Rei’s next location is further away. He/she can be found at the south-west corner of Horseshoe Plains. From where you fought and captured the lone Shinx, head east along the riverside. Here, Akari/Rei will suggest taking on the aggressive Buizel nearby.
Finally, Akari/Rei can be found north of the previous location, in-between three Apricorn trees.
Laventon will reimburse you for all your hard work. (left), Additionally, he will update your Pokédex progress. (right)
Laventon will accept your survey report and give you money based on the number and levels of Pokémon you’ve caught etc. Furthermore, he’ll update your Pokédex progress, tallying up any new Research Tasks you’ve completed and awarding the corresponding amount of research points.
Back at the village, make your way to Galaxy Hall, straight ahead and on the right. Inside, report your day’s hard work to Captain Cyllene. She’ll take a look at your Pokédex progress and upgrade your Expedition Rank if you’ve earned enough research points. On this occasion, she will promote you to the First Star rank.