Here is the full list of all 31 Chicken Police achievements.
Complete the first chapter
Steal that fancy whisky from the Czar Club
Visit the Hop-Dog after the first Police scene
Score at least 5000 points at the shooting range
Complete the second chapter
Complete the third chapter
Complete chapter four
Reach the ending
Get a "Living Legend" grade on a questioning
Get a "Frank Drebin" grade on a questioning
Find all 10 Chicken Police novels
Get all the collectible extras
Visit all the limited locations
Complete all the questionings with "Living Legend" results
Talk to Marty about his feelings before confronting Wessler
Get all codex entries
Get all personal informations
Talk to Marty about the case that separated the Chicken Police
Collect all the songs for the jukebox
Get the secret ending!
Talk with all the characters in the game
Get all the 58 art gallery pictures
Die at least 3 times on the burning ship
Kill the 2 lights of the enemy car in one of the car chase sequences
Help Mort get a room for the night
Get all the cutscenes of the game
Disturb Bloodbolye's peace at least three times
Get to the point where Natasha kills Albert Wessler
Ask Natasha about Ibn Wessler in her room
Talk with the "super-fan" nurse at the asylum
Finish the game with 0 failed questionings