Having trouble getting this on your own? Legit?
Well why don't you just sign a second controller and use the second character to get clues, and rumor points to figure out the case. Once you know the place, the weapon, and the person, use your main character and get enough rumor points to start a rumor. Then just input 2 of the correct answers into the rumor( don't do all 3 correct answers as you will void the achievement and have to restart). This will turn them green on your sheet. Now just remember the third correct answer, or refer back to your guest account.
Note: you must have only 2 green marks on your sheet in order for this to pop. No more, no less.
Also this is possible and way less time consuming to get in quick game, rather then a full game. But ultimately it's up to you!