Here is the full list of all 13 LA Cops achievements worth 1,000 gamerscore. It takes around 6-8 hours to unlock all of the achievements on Xbox One.
200 criminals killed.
100 criminals killed.
All criminals arrested in at least one level.
Finished a level without losing any Cops.
Level completed with no damage.
Complete all 8 main story missions.
Complete all the game missions in normal mode.
Kill 400 criminals.
Kill 600 criminals.
Kill 1000 criminals.
Complete all the game missions in Nightmare Mode.
Complete all the game missions in Hardcore Mode.
Fully upgrade any Cop.