Multiple Kinks to Unkink

First a one time killer is not a serial killer... So you want to know why he would kill again, go back to his first killing, why did he kill his girlfriend? (personally I think this is a poor choice. Serial killers as a rule are smart, smart enough to know that if their girlfriend dies under suspicious circumstance they are going to the head of the list! Do a little research on serial killers and it's far more likely that they picked someone at random.)

Security on board a ship, is different than a small police force. Security is a private police force, who serves the needs of it's employer. Job number one, is making the ship appear safe. If you own a ship and word gets out that their is/was a serial killer on board your ship how many passengers do you believe, will want to come on your ship? I believe a truly smart killer would be smart enough to know that if he can make his killings appear to be an accident the security force is likely to accept that view point, at least publicly. So your killer is likely to believe he is very smart, a genius if you will. And he will get his satisfaction, his pleasure if you will out of outsmarting the security force. His persona will be a very handsome man, who is rich, a desirable catch, perhaps a doctor, an actor, someone that women want to meet, want to catch. That can give him access to his victims. But his victims will not be people he is seen dating... The would point back to him, give things away to easy.

So I believe he will derive pleasure from making your security force look like keystone cops. He would want horrible ways to kill someone, but that could be seen as an accident. Perhaps his first victim will be a drunk, that manages to eject himself into space. One day he is there on board, and the next he is gone.... But no one really notices that he is gone, in the first week. So this kind of infuriates him, and his next victim must be a little bit more noticeable...

In my opinion yes. Also neither one his any authority, any real power, there appears to be a significant lack of reason for the security force to accept them.... Me I might make one a coroner, who the serial killer starts sending hints to because he feels the security force will never catch him. But the hints would have to be of such a nature that she can't really prove she got them or they are real. As an official she has some power, authority, but she can't really take over the investigation. Or perhaps I'd have my serial killer frame her friend, making it appear that her friend is guilty, and it forces her to defend her friend.... She should have insulted the serial killer's intelligence. I'd also think about making my serial killer a women. Again a very beautiful woman, who is successful and very desirable. Twist within twist... Nothing is what it seems. Perhaps our coroner is a disgraced coroner, who messed up her last case? Or at least it appears at first that she messed it up? When actually there was a crooked cop, that cooked evidence, unbeknown to the coroner...

So the ship wants to suppress evidence that there is a serial killer on board.
The serial killer wants/has to kill in horrible ways, each one more gruesome than the last, but that could appear to be an accident.
The serial killer feels that the security force is just way to dumb, and no real challenge for him/her.
The serial killer invites our hero in to the game, perhaps because they feel they where insulted. And sets the hero up with knowledge that lets them know there is a serial killer, but the security force, doesn't want to accept this. They'd rather have it appear that there were a series of unfortunate accidents on board. we need a reason why the hero's opinions can be dismissed.

Hope that helps.

Sorry, space ship, but a cruise ship security force would be pretty much the same right?
Thank you for your help!