Here is the full list of all 28 Police Simulator: Patrol Duty achievements.
Search the trunk of 1 car
Find John's taxi. Or what is left of it.
Have 1 criminal being taken to prison
Frisk 1 citizen.
Identify 1 citizens.
Find the Doughnut shop.
Find the place with the Roman Numerals neon light.
Find the giant dice.
Find the winged statue.
Find the Chinese Shop.
Find John's Christmas present.
Find a Police badge.
Find a blue ice industrial drum.
Find the Owl Graffiti in the seedy part of town.
Find the Owl Stencil in the city's port.
Find the Owl Painting in the "safest" place in town.
Find the Owl Poster in the suburbs.
Find the Owl Towel in the beach.
Write 1 ticket to badly parked cars
Write 30 tickets to badly parked cars.
Have 6 wrecked cars towed.
Identify 35 citizens.
Frisk 30 citizens.
Frisk 50 citizens.
Search the trunk of 20 cars.
Search the trunk of 30 cars
Have 20 criminals being taken to prison
Have 30 criminals being taken to prison.