Lost Judgment

TownGo City Missions are (unsurprisingly) completed by exploring the city, having fights, eating and drinking, and other activities the city offers. You should get this naturally through gameplay. I got it early in chapter 2. Skate everywhere, play minigames and eat at cafés/bars whenever you lose any health.

The first 20 missions I completed were:

• Half-Marathon Man (Travel 21km on foot or skateboard)
• Marathon Man (Travel 42km on foot or skateboard)
• Skater (Earn 10,000 points in skateboarding)
• Pro Skater (Earn 30,000 points in skateboarding)
• Nice Guy (Return 1 lost item to its owner)
• Good Samaritan (Return 5 lost items to their owners)
• Click! (Snap 10 photos with your smartphone)
• Big Eater (Eat at restaurants 10 times)
• Inebriated (Drink 5 different types of alcohol in venues)
• Town protector (Defeat 100 enemies who pick a fight on the streets)
• Ex Actions 10 (Activate an EX Action 10 times in battle)
• Ex Actions 50 (Activate an EX Action 50 times in battle)
• Tiger Cub (Defeat 50 enemies with Tiger style)
• Crane Hatchling (Defeat 50 enemies with Crane style)
• Snake Broodling (Defeat 50 enemies with Snake style)
• Mad about minigames (Play 10 minigames)
• Minigame crazy (Play 20 minigames)
• Mr minigame (Play 30 minigames)
• Gotta get 'em all! (Gathered 100 materials)
• Gotta get a ton of 'em! (Gathered 200 materials)

CyricZ's amazing guide on GameFAQs has a list of all the city missions with tips:
https://gamefaqs.gamespot.com/ps4/320117-lost-judgment/faqs/...