Save Files...
	Various Steam Achievements...
	What's the Problem...
	Who Counts...

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.

Note: 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.

Example:
"thievesSpawned":2,
"achv_arrest":45,

Complete the indicated task to unlock the achievement.

Achievement	How to unlock
...And Justice for All	Sooner or later everyone pays for the sins.
Adiós Muchachos	Und Ich bin mit my friends from old times.
Amelia Earhart	Could it be real?
Among thieves	That's why you graduated from Police Academy. To catch twenty shoplifters.
Born to be wild	Lookin' for adventure and whatever comes our way.
Cat person	Because some people just want to watch the world meow.
Chasing pavements	I bet people love you after issuing hundred tickets.
Compulsive ticketer	You love this job, don't you? That's what 250 issued tickets means.
Fahrenheit 451	Who knows where it comes from?
Fetch	And let's see what happens. Will PETA intervene?
First time is not a crime	It's only a bribe if you're caught. Don't get caught ten times.
Gotta catch'em all	Stealing bubble gum is a serious crime. Catch fifty shoplifters.
Have a blast	Well done, Mr. Bond.
Ice ice baby!	Just chill out.
La Cucaracha	He has a large family to support.
Made man	Beginning of a beautiful friendship...
Money talks	After fifty bribes, consider yourself an addict.
No heaven for you	He could have washed his pants, not his brain.
OG	They accept you as you are.
One for the team	And can you tell me please how to get to Sesame street?
Raging Bull	If you win, you win. If you lose, you still win.
Rated R	Tell them to volunteer. Tell to drop out of college and join infantry.
Run Kelly, Run!	Who's faster? You or ten shoplifters?
Secret sauce	This is why you should look at ingredients from time to time.
Slav squat	And remember how to recognize a Western spy!
Someone should debug this game	...and you just did that!
Sticky fingers	Take twenty bribes and be happy. And don't worry.
Sword fight	This is for movie nerds. Who gets it?
Use the back door	Sometimes that's the only way. At least that's what she said.
Weapon of mass destruction	And still some dream about having one.
While there is still no wall	...so go and enjoy some chimichangas.
You've always wanted to do this	Hit the street and write fifty tickets.

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.

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.