These days you won't get a sniff at a job without a criminal justice degree and courses in related areas, such as forensics, psychology, sociology, and criminal investigation.
Once you get a job, you will receive highly specialized training in all of the skills you'll need to get them goons who commit crimes. You'll learn surveillance techniques, get weapons training, learn interrogation methods, and practice raids.
For this reason, military experience is also a great precursor to becoming a criminal investigator. If you can handle live combat, you got this!