A few tips that will hopefully help with this rather frustrating achievement.
What's the Problem
This achievement is supposed to be awarded for catching 50 shoplifters. However, its description is inaccurate and if taken quite literally one could spend many hours and never get it. You can't grind it by rewinding days, it is achieved in single playthrough and the rewind function can be used to get a better result if you missed an opportunity to arrest someone. Remember to start over or rewind immediately. If you rewind more than just to previous day, you'll loose all your progress after that day.
The next section contains minor spoilers!
Shoplifters alone aren't enough to get this achievement. Only 27 thieves spawned in the playthrough I got it. Catch them all but keep catching other baddies as well. Catch Crew members tagging the walls and try sorting out local problems as they often result with arrest opportunities that also count toward this achievement. Arrest mobsters trying extort money from local businesses, the boxer who caused disturbance, the drunken guy who stumbles to the car you were looking for, the mobster who tries to bully you to forget those taxis they're using to distribute narcotics. If you see arrest option, use it. There's also a dealer standing on different corners every day. You can buy drugs from him but you can also arrest him. But if you want to arrest him every day be careful as you'll quickly get yourself in a lot of trouble with the Crew. Do a favour for them every now and then. The same goes for the Mafia as they won't be happy with all those arrests after a while either.
You can follow your progress toward this achivement by looking into the game's save files.
You can find them on your C drive, this is the path on my computer C:\Users\USER NAME\AppData\LocalLow\Pixel Crow\Beat Cop\BeatCopSaves18. You may need to change your folder settings as the AppData folder is normally hidden.
After each day you can check how many thieves spawned that day and if you missed any and also check the total number of arrests. Pictured are my days 18 and 19. I was going into day 20 having arrested 1 thief and a couple mobsters extorting money and someone else, a wall tagger I think, bringing the total number of arrests to 49. On day 20 the achievement popped right after I arrested another thief.