This achievement is very simple and is not missable.
A street crime case is a random event that pops up every once an while that asks you to go to a specific location to deal with a criminal. This may be different for a few people, but the first street crime case that you should obtain pops up as soon as you start driving your cop car with the siren on once making traffic detective, which is the second rank in the game after regular cop. Dispatch will call you and a prompt will show up asking you to press
. Accept the call with A and follow the marker to the crime scene, which marked by a yellow figure on the map. Go to the location and you will get a cut scene and then prompted to do something, such as chasing a suspect. Once you have accomplished the objective and another cutscene passes, you will unlock this achievement.