To earn the Expert Crime Fighter achievement/trophy in Gotham Knights, you must “Prevent 250 crimes in Gotham City”.
As can be expected of a well-run polity like Gotham City, crime abounds when the sun goes down - you’ll usually find at least half a dozen premeditated crimes every patrol, as well as several opportunistic crimes in each district. You’ll need to clear Gotham City of crime fully numerous times to hit the 250 crimes this achievement requires, but it’s stopping crime is something you’ll end up doing as part of the main questline and if you want to earn the achievements [Not On My Watch], [Protector of Gotham] and [Dressed to Impress], just to name a few. Aside from the game’s case files, the open world crimes plaguing Gotham City are kind of a core gameplay element.
All that being the case, don’t worry about “Expert Crime Fighter” too much. All crimes count towards it regardless of whether it’s an opportunistic crime or premeditated crime, what type of premeditated crime it is, and what faction is perpetrating said crime, and there’s a lot of them each patrol. Work on other objectives and if this achievement doesn’t pop before you get everything else (which is unlikely), just start new patrol and hunt down those naughty white triangles on your map until it does.