This is a complete guide and walkthrough on how to get the Unsolved ending/achievement.
This is one of the easiest achievements/endings to get in The Deed II and does not require any evidence at all. The main goal of Unsolved is to make sure that nobody is found guilty of the crime.
Obviously, this guide contains spoilers for the game and provides a full walk through for getting the achievement, so if you want to do this on your own or see the game for yourself, please stop reading.
Keep in Mind
One thing to keep in mind for this ending (and most other endings that involve you getting away) is to stay as calm and civilized as possible. Don't engage in fights and try to sympathize, reply to every statement calmly, and don't pick risky dialogues that might lead the person to become angry. This can raise your suspicion and make the inspector want to "dig deeper" into your past.
Make sure to keep track of the time. For this guide, I have chosen to "do the deed" when Frank is in the balcony (top floor, room to the right, white door). He will be there, unaccompanied from around 9:48 - 10:00 PM.
First Thing's First...
When you start, you want to make sure that you are completely honest in your responses with Marie Dupont (the first girl you meet). Tell her your real name and tell her that this is not your first time in a brothel.
When you start, make sure to NEVER INTERACT WITH FRANK. This will make the inspector believe that you know him from before which raises suspicions on you. For an ending like this, it's crucial that you prevent them from having any doubts of you.
Feel free to interact with anyone else, but once again, make sure that you are completely honest, not provoking, and don't talk about others while that person is in the vicinity.
Before You Do the Deed...
Remember, you're not here just to kill him. You're supposed to be here to have a good time. You can choose to either go to Mistress Chevalier (top floor, room to the left) or Atma (bottom floor, room to the left), whichever satisfies your *fantasies*. You could also go to both but you will be broke by then because you only start off with 20 francs, and each one costs 10.
You also want to ask the bartender Maurice for a drink. This makes your presence more natural to the inspector and makes him suspect you less. This is also why you may want to not spend all your money on the girls, as you won't be able to buy a drink from Maurice.
You could possibly use the revolver or the poison for this ending, but the most suitable weapon of choice is the wrench. This is because two people (Jean and Aspasia) use the bathroom. This makes the inspector suspicious of them but not suspicious enough to convict them of murder, which is exactly what we need for this ending. Make sure to enter the bathroom and take the wrench before 9:40 PM, because Jean will forcibly enter by then, whether you're in it or not.
Doing the Deed
The time has come. You've pleasured yourself, had your drink, and picked up your weapon. Now, you must finish Frank once and for all.
Because you weren't occupied in conversation or planting evidence, you should typically have plenty of time left. It is best to stay in the salon until 9:50 PM. Aspasia will be in the bathroom, Frank will be in the balcony, and everybody else will be in their original spots. If you try to move around earlier, Aspasia might spot you on the top floor and this gets you killed in the future.
Head to the balcony and take his life. The Deed has been done. But you have to escape. Killing with the wrench gives you 10 seconds to escape. This is enough time to rush out of the bedroom and make it to the middle floor. Nobody will spot you there so you can safely lie and say that you were in the Medical Room. By that time, your deed will be discovered.
This is the final part of your act and the most decisive one. Any wrong choice can get you executed, so be careful with the interrogation.
Be cooperative at all time. Make sure that you tell the inspector that you have never seen Frank before, despite you both arriving at the same time. You should also say that you had come to the brothel for the "usual reason". This will be supported by your visit to Atma/Chavelier's room.
When the inspector asks about your location when you heard the scream, you have to change your answers based on where you were and if somebody saw you. If you were spotted by Chavelier, the inspector not ask you the question. If you were not, lie about being in the Medical Room. The bathroom was occupied by Aspasia, so you can't lie about that. The Medical Room stays unoccupied throughout the entire time so you can safely say that you were there, even if you weren't.
The inspector will bring up different evidence that is not relevant to the case and discuss the murder weapon. This is where the wrench comes into play.
If you did everything correctly, the inspector will not have any hard evidence against anyone and he will also find no reason to suspect you. You're free to go.
The rest of the ending is dialogue that doesn't change anything, and you should have gotten the achievement by now. Congratulations! You completed one of the endings in the Deed II.