I had this issue in one of my rental. Actually the building my wife and I were living in. The original neighboring tenants were quiet no problem newer ones slightly louder. The first wall I did was inbetween the living rooms of both apartments. That wall consisted of standard 2x4 stud and 1/2" rock on both sides. I stuff the wall the sound deadening fibermat insulation available to lowes.(I want to say Owens corning product). While that did yield improvement it really was still louder then I was happy with. In the bedroom I actually furred the wall out to 7" thick and put in 2 layers of the sound deadening insulation with the joints staggered. This yielded a more livable result, but honestly I’m still not thrilled about it. However we no longer live there and the materials I used were expensive enough I have a feeling you will find that the cost of this project might be more then you think. Materials cost have gone up substantially. Anyway good luck if you need a hand just shoot me a text you have my number.