Here is the full list of all 24 Giant Cop: Justice Above All achievements.
Attend your first callout
Arrest the wrong people. On accident, right?
Throw 50 pedestrians into the ocean
Destroy 150 cars
Attend all of Agnes' callouts
Collect all 210 Micro City Police Badges
Arrest 10 nudists
Play with all toy types in the game
Protect the city from Spanksy's lies
Arrest 150 criminals
Arrest 75 criminals
Arrest 25 criminals
Blast a pedestrian out of Micro City using the tennis racket or baseball bat
Land a criminal in jail from a mile away
Throw 100 paint barrels
Shake down 75 pedestrians
Complete the Capital Square district page in the notepad
Complete the Rusty Mills district page in the notepad
Complete the Microvista district page in the notepad
Complete the Golden Sands district page in the notepad
Take part in a mass surveillance operation
Spend 15 minutes playing with big kid's toys
Travel to every district in the city
Get to the bottom of 2 cases in 2 minutes