After finding all of the clues and piecing together all of the evidence you are left with 3 final deductions. Selecting any of them and finishing the story will get you this achievement. You just have to finish the case, you don't have to get what the game considers the "correct" choice.
The correct one is:
*** Spoiler - click to reveal ***Mr. Butcher is a murderer.
He planned the heist and killed the gang members he worked with to get all the money for his sick daughter. You can either absolve him and he will leave town with his daughter or you can arrest him.
The wrong deductions are: