This is actually tougher than it sounds since the game is pretty forgiving. The way I got this was to build up a large city. I then saved the game so I could reverse the damage.
1. Turn off or destroy all police buildings.
2. Raise the industrial, commercial, and office tax rates to their max and if you have policies unlocked implement the tax increase policies for these categories.
3. Lower the residential tax rate to the min (1%). This way people won't necessarily flee.
4. Keep your other services in place so people don't run away from your city. You need them to stay.
With these changes made I had the crime rate hover between 45% and 55% for the duration. On 3X speed two years is approximately 1h20m so you'll be sitting there for a while.
This is a good trophy to do in conjunction with unlocking the unique building that requires unemployment. Increasing crime is basically about increasing unemployment but getting the people to stay.