OK. First, I have to agree that the person you describe is NOT a psychopath but is a Narcissist. The posts suggest a number of ways of dealing with Narcissists. Psychopaths, however, are a whole other ball game. For one thing, they are not all alike, and I have never met one who was the “serial killer” type although I am sure they exist, they are just pretty rare (thank goodness). In my rather long life, I have been in relationships with two psychopaths. They were both handsome, charming, easy to be with and very good and considerate lovers. Not the picture you expected? Well, let me add, they also could tell fantastic lies (of the tall tales variety), they did not concern themselves with normal morals (if they found something, like a wallet, they would take the cash and throw out the wallet, they did not show any concern for their friends if something bad happened, etc). What they were was imminently rational. One of them, let’s call him Jack, was my first lover. He was a good choice and was knowledgeable and considerate. For other stuff, not so much. We did not live together but we were together a lot. I was in love. He was attentive, did the usual “trying to impress you, guy type displays like wheelies on a motorcycles, etc,” and was very easy to talk with and be around in general. My mother thought he was the most personable man I ever dated. My father didn’t like him but didn’t know why. After we had been dating for about a year, I heard from a friend that she thought he was married. My heart sank, not just because he belonged to someone else, but because I would never knowingly have done something that might destroy someone’s marriage. I cried and by the time he arrived I was a mess. Of course, he knew something had happened. So, our conversation went something like this (btw I am a math/science type of thinker so if my part of the conversation seems strange, it is because reason has a strong appeal to me). So, here we go:
Me “Susan told me that you are married.”
Him “I am.”
Me “Why didn’t you tell me?”
Him “You would not have gone out with me.”
Me (stopped short and thinking that that made sense) “Then why didn’t you tell me later?”
Him “You would have stopped seeing me.”
Me “So, I guess it is over.”
Him “I guess that it is, but I would have liked for it to continue. It is too bad you found out.”
I did stop seeing him. He had one of my gas credit cards and used it occasionally. I paid it. Then he started charging other stuff on it and I called him.
Me “You are charging more than gas on my cc. I didn’t mind covering you for gas even though we were through, but I am not going to pay for all the other stuff”
Him “ok”
Me “So, here’s the deal. You mail me my cc back and I will pay what you charged right up to this minute and nothing more. You charge more on it or don’t mail it back and I report cc fraud and get the police interested in you. I don’t want to do that because I do still care about you so please send me my cc.
Him “ok”
And he did send me my cc without charging more on it.
Two years later I get a phone call from 1000 miles away.
Him “I am in trouble”
Me “What happened.”
Him “I slept with a girl and she was old enough, but her brother is telling her to claim rape.”
Me “No way you would ever rape someone, I believe you.”
Him “I am in the slammer. This is my phone call. The brother says if I can give him $1000, they will drop the charges”
I checked, he was in the slammer. Talked to the brother, and he was pulling a blackmail scam, but he knew what he was doing. We made agreement about the money. I sent it. Jack went free. He called me and thanked me. He did not bother to say that he would pay me back because we both knew that would never happen. I said, next time call someone else. He said, ok. I never heard from him again.
So, a Psychopath but not an evil person, all in all a fun, likeable person with some baggage. From everything I could tell, the correct response was to use REASON.
The other guy was a bit scarier, had killed people for the USA, but again was able to respond to REASON especially if you point out his own self interest.
So, this may be anecdotal, but it is my experience in dealing with Psychopaths. I like them a lot better than the other personality disorders like Narcissists and Borderline. At least you have fun while it lasts with them.
So, finally to answer your question. If you are dealing with a Psychopath do not try to bring them down. Just figure out what they want, reason with them and appeal to their self interest. That is my advice in a nutshell.

First off, we have to make a distinction between psychopaths and narcissists. I see some posts in quora that intertwine these two diagnostic categories.
Narcissists love themselves. They construct a delusion that they are perfect and the best and attempt to get others to mirror back to them that they are wonderful. There is a pseudo-self that is created. Narcissists seek adoration, validation, and lots of attention. They are very concerned about what others think of them and are vulnerable to rejection, ridicule, being upstaged….. If any of these circumstance occur, they experience what is called a “narcissistic injury” resulting in outright aggression or passive-aggressiveness. Sounds like someone we know about who has been in the news lately (hmm..).
By contrast, psychopaths do not care what others think. They are concerned about “the hunt.” They love to manipulate others by first gaining trust. They are not emotionally dependent on being admired or recognized. They are covert. Psychopaths do have a strong ego which means they have a strong sense of self. Psychopaths are generally more dangerous than narcissists. Ted Bundy is a good example. Narcissists seek attention for its own sake. Psychopaths seek attention in order to get something in return.
So attempting to bring down a psychopath is not easy. You would have to have some training in psychology/counseling in order to have skills in empathy, reflective listening and probing. You have to get on their good side first and develop rapport. Once this is established, you may see signs of vulnerability but this can take a long time to get there. The goal would not be to bring them down, but to try to understand and chip away at their defenses. – Carlos V. Guzman, PhD

Unless a) you have good reason b) are sure of your diagnosis based on training and c) you admit the chance of not succeeding with a lot of damage control etc, DON’T BOTHER. Layman who has seen them at work, and has the simple method – remove them from your sphere of operation, or you from theirs. Dust off your shoes, retreat, do not pass go. They may try to follow, but a strict discipline not to engage or turn back to face them. Demonstrate control of your affairs, full stop. They meddle, don’t react. Hold the line. Be resolute and …. good luck.

You definetly can, but you should never try!
There’s a direct and a subtile way, first off the dorect:
I’m sure every psycopath, no matter how narcisstic he is has a weakness he can’t deny, and if you still want to break one down, look for it and confront him. I can’t garantuee you’ll find one, just give it a shot.
The subtile way:
Be unpredictible, completely random, let a dice decide. Many psychopaths (including me) study the behaviour of people and often understand what emotions do with them. So if you don’t behave rational nor emotionally, we’ll have a hard time understanding what’s going on. Depending on the level of narcissm, the psyhopath will ignore it (you reached nothing) or questions himself an his abilities (maybe some sort of a win for you, but not on the long term).
If you somehow managed to break one down, for example get him insecure, watch out! As Jacob already said, “Psychopaths make great friends and horrible enemies”. If you make a psyhopath angry, he’s likely to hurt him very bad (not physically but mentally) and you’ll wish you never knew him and then never wastes a single thought on you afterwards.