Here is the full list of all 41 Lamplight City achievements.
You're so annoying
Kept your promise to Mrs. Hanbrook
Played a familiar melody
Got kicked out of Sabine Martin's apartment
Read Madame DuPrée's poems
Accused Albert Martin of Madame DuPrée's attempted murder
Accused Juliette Montgomery of Madame DuPrée's attempted murder
Accused Guy Dumas of Madame DuPrée's attempted murder
Revealed Madame DuPrée's true nature
Fixed the boiler without any help
Spoke with Roland Deveraux
Learned about Mrs. Davis's hobby
Accused Malcolm Harris of kidnapping his own son
Accuse Arthur Devins of kidnapping the Harris baby
Accuse Linda Walker of kidnapping the Harris baby
Successfully located Linda Walker
Showed Desiree's ashes to someone who wasn't Dr. Edwards
Tricked Jonas Usher
Gave Charlotte Robineaux a music lesson
Concluded that Desiree Lathan's death was due to spontaneous human combustion
Accused Roger DeVay of murdering Desiree Lathan
Accused Margaret Andrews of murdering Desiree Lathan
Told Patrick a story
You voted!
Discovered the truth about the cooping scheme
Accused Jimbo of murdering Ronan L'Espaye
Accused Tom Puffin of murdering Ronan L'Espaye
Sang a popular drinking song
Confronted the Justice Killer in his own home
Told Adelaide the truth
Told Angela Maxwell about your problems
Checked yourself into Riverview Asylum
Ended up in jail
Declared a case unsolvable
Read every book in the game
Found every single clue and document in the game
Completed the game
Played through the entire game without opening the casebook
Correctly solved every case
Every friendship has one
Eavesdropped on every conversation