Lost Judgment

Complete all of the 42 available side cases (DLC side cases do not count). Some are story-related, and other ones open up in Chapter 3. The rest are attached to Girls' Bar and the Emily girlfriend questline.

Here are all 42, in (roughly) the order you can get them. You can check your progress on the 'Case file' app, under 'side cases'.

Chapter 1

1. Skateboard Detective vs. the Reseller (unmissable story-related story)

Chapter 3

2. The Falling Man (unmissable story-related story)
3. The Café Robber
5. Where is the Time Capsule?
7. The SRC's Hunt for the Truth (need Buzz Researcher keyword ‘UFO’)
8. The Invisible Burglar (need Buzz Researcher keyword ‘stalker’)
9. The Body Model Walks at Night!!! (need Buzz Researcher keyword ‘body model’)
10. Dueling Dojos (get from the Kamurocho detective agency board, where it’s called ‘The Saga Continues: Ryan's Rival Appears!’)
11. The Forbidden Taste (get from Yokohama detective agency board)
12. Paradise VR Unlocked!
13. Paradise VR Upgraded! (must have completed Paradise VR Unlocked!)
14. Let the Drones Fly!
15. Extracting the Past (unmissable story-related case)
16. Extracting the Truth (must have completed Extracting the Past)

Chapter 4

4. Trying the Patience of a Saint
21. Dastardly Detective: Introduction (unmissable story-related case)
22. Dastardly Detective: The Wandering Bug (need Buzz Researcher keyword ‘noise’)
23. Dastardly Detective: Grasping Attention (must have completed ‘The Wandering Bug’)
24. Dastardly Detective: Before the Torch Burns Out (must have completed ‘Grasping Attention)
35. Between Blood and Booze (part of Girls’ Bar, unlocks once you get detector and have School Stories appeal level 4)
36. Big Shame Hunter (part of Girls’ Bar)
37. Random Fandom (part of Girls’ Bar)
38. Step By Step (part of Emily S. Mochizuki’s girlfriend quest, which unlocks when you complete Girls’ Bar)
39. Broken Barriers (part of Emily S. Mochizuki’s girlfriend quest)
40. We Mend, We Grow (part of Emily S. Mochizuki’s girlfriend quest)
17. A New Partner? (unmissable story-related case)
6. Where the Kappa Roam
19. Flight of the Game Creator (get from Yokohama detective agency board, where it’s called ‘Our Runaway Game Director!’)
20. A Particularly Hardcore Demo Event (must have completed ‘Flight of the Game Creator’)
18. Chaos of the Masked Writer (get from Yokohama detective agency board, where it’s called ‘Please Investigate a Corporate Spy’.)

Chapter 5

31. Squirrels Just Wanna Have Fun
32. Big Squirrels Don't Cry (must have found all 55 squirrels)
25. Dastardly Detective: The Eavesdropping Wallet

Chapter 6

33. Curse of the Amasawa Family Heirloom

Chapter 8

26. Dastardly Detective: Seiryo High in Danger (must have completed 'The Eavesdropping Wallet')
27. Dastardly Detective: From the Pit of Despair (must have completed 'Seiryo High in Danger')
28. Dastardly Detective: The Secret Ingredient (must have completed 'From the Pit of Despair')

Chapter 9

29. Dastardly Detective: The Final Night Flight (must have completed 'The Secret Ingredient')
30. Dastardly Detective: Closing the Case (must have completed 'The Final Night Flight')
41. Takayuki Yagami: Evil Detective? (must have completed all the School Stories)

Finale

34. My First Errand (get from Yokohama 99 jobs board)
42. A Final Request -Reprise- (unlocks once you’ve completed all other side cases)

For a full list of side cases, including how to unlock and complete them, see CyricZ’s excellent guide on GameFAQs:
https://gamefaqs.gamespot.com/ps4/320117-lost-judgment/faqs/...

The final side case is a fight against your old mortal enemy, and has its own associated achievement: