Eddie Murphy did not receive an Oscar nomination for portraying Axel Foley in Beverly Hills Cop.
Eddie Murphy now is considered to bit of a wash up as he rarely has a successful comedy. Back in the 80's when this film came out though he was considered to be on top. This does not mean though Murphy was necessarily the greatest actor at this point though. In Beverly Hills Cop he portrays the Detroit cop who makes his way to Beverly Hills to avenge his friends, and there are really two sides of this character the serious side and the Eddie Murphy side.
Originally the film was going to star Sylvester Stallone, and it is pretty easy to see how the film would have been with Stallone in the lead, it is also easy to see the ways Murphy presence changed the film, but as well to a degree was forced to stay in line with the original idea for the film. There are basically two types of scenes for Murphy in this film which really do not overlap in the way they probably should which are the serious and the humorous ones, and yes there are far more serious scenes than one would expect from a Eddie Murphy comedy.
I might as well mention Bill Murray as a great example of an actor who is able to traverse through the serious and the comedic without a problem as he did in this year in Ghostbusters, as well as later on in fantastically in Groundhog's day. Murphy though pretty much separates them, trying maybe a little to put some comedy in the more dramatic moments, but mostly that just involves him doing his somewhat odd dry heave laugh which he always does in the more serious scenes of the film.
Murphy I can't say is all the convincing in any of the dramatic moments such as when Foley is hanging out with his friend or later reacting to his death. There is not any conviction in his performance, nor is there anything in his performance to make their relationship mean anything. Murphy though very well could have taken the route of always going for laughs, but he does not instead he actually tries to be convincing as the character and he is a bit awkward in these moments.
What made the film popular though I'm sure are all of the comedic scenes which apparently Murphy improvised for the most part. This actually seems quite obvious since Murphy is on a much better level during these moments. He has a high energy, and he really does try to make the most of riff he can come up with. To Murphy's credit as well he does make these seem as Foley's method rather than simply Murphy being Eddie Murphy.
It is hard to say that every one of the scenes that Murphy humorously goes through are downright hilarious, but most of them are quite amusing, and some of them are hilarious. It is probably rather safe to say that without Murphy this would have had very few if any redeeming features, since his full fledged comedy scenes are by far the best scenes in the film. Still I cannot forget that the serious scenes are certainly very lacking, something Murphy as well did better in films before and after this one.This is not a bad performance by Murphy becuase when he is funny he is funny, but that is really the best that can be said about this performance, which may be enough I suppose.