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.
All game missions completed in Nightmare Mode.
All game missions completed in Hardcore Mode.
All game missions completed in normal mode.
All 8 main story missions completed.
1000 criminals killed.
600 criminals killed.
Fully upgraded a Cop.
400 criminals killed.
All criminals arrested in at least one level.
200 criminals killed.
100 criminals killed.
Level completed with no damage.
Finished a level without losing any Cops.