I have been trying to work on myself but I feel as if nothing I do is enough for him to realize that.
But working on yourself is not for that purpose. It's for you, not for him to notice or approve of. If you are working on yourself so he will change, it isn't really yourself you are working on.
I agree with everyone else, and I'm sorry. A psychopath will not change. The only way they will sometimes act as if they had empathy is if they can be made to see there is something in it for them, but the empathy itself is never going to be there. Trying to get a psychopath to love you is like asking an elephant to turn into a zebra.
I spent several years with a man who turned out to be a controlling, manipulating narcissist. Slightly different symptoms, but again, the kind of person who won't change because they don't see any need to. That relationship destroyed me almost completely and caused a lot of damage to our daughter, who witnessed the abuse. People kept telling me to leave, but I stayed because he filled a need in me. In the honeymoon phase, he showered me with the "love" I never got from my family, and desperately needed. That feeling was like a drug, and longing for it took over my life in the times he withdrew it - which got to be longer and longer until it was all the time. Until I gathered up the last of my strength and left.
I think the more productive thing to do here would be look at why you feel the need to be with someone who treats you this way. What was your life like before you met? What need is he filling for you? I know that "you can't change anyone else, only yourself" has become a platitude, but unfortunately it's true.