The quickest way to get the achievment if you already beat the game is to replay the first traffic desk case. When you replay a level, you automatically start the case with 5 intuition points.
The intro cutscene will be a bit long, but after it is over let your partner drive you to the crime scene. You can skip your partner's conversation while driving by pressing the "a" button. Examine the wallet and glasses next to the tree behind the car, which is next to "C". Then you can examine the pipe which is next to "B". Finally, you can examine the car. Talk to the person who discovered the scene.
At the beginning of each question, use an intuition point. The answers are all truth except the wallet question, which you should doubt.. When you finish the achievment will pop.
I would like to thank snugglebait, ClansR4diks, napoleon1066, and JusZen for correcting errors I have made in this solution. I also would like to thank OCChoppers for leaving constructive feedback.
Please leave comments on how I can improve this solution. I am always open to suggestions. Also, if you give this solution thumbs down, please comment why.