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