Fall City Ranger Base
Seeing as you completed your mission successfully, Joel decides to officially promote you to Ranger Rank 2! With this rankup, you can now use the Fighting Poké Assist! Joel asks that you wait while he and Hastings go to speak about something on the top level. Talk to Leid and Keith, and then Aria will enter. After you've introduced yourself to all 3, Hastings and Joel come back from their talk, and they inform you that all of Fiore's Rangers will work together to stop whatever Team Go-Rock is planning on doing with the Super Styler.
As Fall City's rangers are gonna be busy investigating Krokka Tunnel, Joel asks that you go around the city solving whatever problems the citizens might have. And so, a new mission begins.
Fall City Case Log
If you walk to the right of the Ranger Base, a girl will interrupt you and ask if you can come to her apartment, as she's been blocked out of her room. You'll need to go help her, but it's recommended that you explore the city a bit more, catching some of the available Pokémon on the way.
You will need to, at the very least, capture a Makuhita. Once you've done that, head east to find the girl standing at the door of the apartment building she lives in. Follow her and you'll see a box blocking the entrance to her room. Use Makuhita to move the box, and you'll find a Venonat in her room.
She asks that you release the Venonat after you capture it, so you do.
Heading out of the house, you'll be approached by a woman who seems to have lost her Skitty, so you decide to help her find them.
Go back into the building you were just in, but this time go up the stairs at the top. Going up to the roof, you'll find your first Skitty!
You need to find 5 Skitty total (so 4 after the one you just caught). However, before you go catch any more, deliver the one you just got to the lady by talking to her next to the Ranger Base. After that, go north and catch the Snubbull, if you don't already have a Pokémon with a Field Move of . From the Snubbull's location, go west past the building and then north to find a Meowth.
Capture the Meowth only if you want to register in the Browser, as it is not currently necessary. Either way, continue going north, into the house. Interact with the Skitty hiding among the plushes, and capture it. 3 more to go!
Head back to the middle of the square, and then go south to the next screen. You'll find a Skitty playing around the fountain, as well as a new Pokémon, Ludicolo!
2 Skitty to go!
From the fountain, head west and then north to find two trash cans. Interact with the one on the right and you'll hear a Skitty's cry. Use the Snubbull (or Makuhita) you captured to bust the trash can open, and capture this Skitty! 1 left!
From the cans, go to the right until you see a Meowth. Capture it and use its Field Move to clear the fence behind which a Skitty is hiding. The Skitty will run away, follow after it to the next screen. You'll walk in on a Researcher doing something to a Machoke. However, you can now capture the last Skitty, and go deliver them to the woman!
Flash a Light
You'll be approached by Professor Hastings' assistant as soon as you walk to the right of the Ranger Base. Follow her to the lab. She needs your help to light up the basement, and reminds you of the Professor's advice that Staryu can be of help to light up dark places.
Go back to the square and head south to the fountain.
Head south again, and you'll find yourself in the starting area of the game, only this time you're able to catch 2 of the Pokémon you saw before, Krabby and Wingull.
You'll also notice the Snorlax that was here before has now left and revealed an entrance to somewhere. Go in there and you'll find a Staryu!
Capture the Staryu and bring it back to the lab. You can use its Field Move to light up the basement by just going in there through the stairs on the top right and tapping on Staryu.
Go out of the lab and to the square, and you'll meet with Aria. You'll hear a Pokémon cry coming from the clock tower, so you go to investigate. Turns out a Machoke is going berserk, and Aria asks that you go capture it.
Machoke is a pretty tough capture, be careful for its punches and for it jumping and breaking your line. You may want to use your partner's assist if available to stun it.
Once captured, Machoke will calm down. And just like that, the town's requests have been fulfilled!
You release the Machoke, and Aria tells you to head back to Ranger Base as she goes back to investigating Team Go-Rock.