New Moon

Kinshicho: First things first, you'll start in Kinshicho. Your objective here is to leave and head west towards Shinjuku. Easy enough.

Tokyo: As you move west from Kinshicho, you'll pass through Tokyo. Keep heading west along the south path, past Kanda-no-yashiro. You'll then need to navigate north and west through some poison areas. After that, it's a bit of a winding path south and then back east-northeast to reach Shinjuku.

Shinjuku - South Entrance: Once you arrive in Shinjuku, head northeast from your starting point. A scene will trigger. After that, go a little west and then north. You'll find a hunter; talk to them and take the elevator down to B1.

Shinjuku - Station - Underground: Move forward from the elevator, and you'll unlock the Shinjuku Terminal. Keep an eye out for a short scene. After it plays, head west at the underground intersection and then go north up the stairs.

Shinjuku - Station - West Entrance: Continue heading west until you move to the next screen.

Shinjuku - West Entrance Buildings: It's a good idea to save your game here. Once you've saved, keep pushing west to the next screen.

Shinjuku - Government Office Plaza: More theatrics will happen here. After the scene, move north, then west, and head down the stairs. You'll need to jump down towards the southeast of the landing, then run south up some stairs. Go east and immediately up another set of stairs. Now, progress west until you see the red flag. You'll encounter a BOSS, Lv 40 Unwinnable. Don't stress about this fight; just focus on getting past it. After the encounter, take the west-most stairwell to the north and then head east back to the previous screen.

Shinjuku - West Entrance Buildings: Continue heading east to the next screen.

Shinjuku - Station - West Entrance: Head down the stairs, taking you back into the Underground area.

Shinjuku - Station - Underground: Make your way east into the Shinjuku Hunter Association.

Return to Kinshicho: With your business in Shinjuku done, you'll need to return to Kinshicho. Use the Shinjuku Terminal to fast travel back. Once you're back in Kinshicho, head to sleep to complete the quest.