Here is the full list of all 13 LA Cops achievements.
Complete all the game missions in Nightmare Mode.
Complete all the game missions in Hardcore Mode.
Kill 1000 criminals.
Complete all the game missions in normal mode.
Kill 600 criminals.
Complete all 8 main story missions.
Kill 400 criminals.
Kill 200 criminals.
Kill 100 criminals.
Fully upgrade any Cop.
Finish any level without losing any Cops.
Finish a level without any of your Cops getting hit.
Arrest all criminals in any level.