Some of the younger fishermen talk of the sea like it is the battlefield or an enemy. But Santiago doesn’t think this way. He speaks of his love for the sea and all its creatures. You can have reverence for an enemy but I don’t think the fish or the sea can be considered Santiago’s enemies: from his or an outside perspective.
Time and old age are his enemies. Santiago still has a fairly youthful outlook on life, but his body is old and this is one of the contributing factors to why he loses the fish. He fights valiantly, but he is overwhelmed by his age as well the long distance he has to sail back.
Although he is older, he is still a great fisherman. He proved it by catching the great fish; even though he lost it. Since he is still a great fisherman, physically weaker but certainly wiser, I’d say one of his other enemies is bad luck. Interpret that any way you want: in terms of destiny or just dumb luck. Santiago relies on skill more than luck. But before catching the great fish, his slump was described as though it was unprecedented in his fishing career. He can always rely on his skill but any fisherman or businessman is subject to a drought or a recession. This is the ebb and flow of social and natural life. In the greater scheme of things, at this point in his life, he fishes because he loves it and he does so in order to survive. Here, I’d say his enemies are the feeling of uselessness and nature itself. He needs to fish to feel meaningful and he loves nature but must combat its effects (his old age and the continuing supply of fish).
This is a very deep question. I don't think that this novel necessarily has an "enemy" in perhaps the sense you are talking about. There are certainly no direct antagonists who try to stop Santiago from achieving his goals. We could say that the fish would be the closest thing that we have as an enemy. The fish of course is desperate to avoid capture, and seems to match Santiago's resoluteness and stubbornness with his own determination to escape. Note how the fish tows the boat for two days before he admits defeat. However, the problem with regarding the fish as the "enemy" of Santiago is that both his struggle and his defeat are matched by the struggle and defeat of Santiago. In the fish's demise, Santiago himself "fails" in his struggle, as the fish is lost to the sharks. Both the fish and Santiago in their own way are dejected and defeated.
Perhaps it might be more accurate then to say that the real "enemy" in this novel is an indifferent universe that gives little weight or importance to our momentous struggles. Santiago feels completely "beaten" by forces beyond his control, and in spite of giving his all into the struggle, admits defeat:
He knew he was beaten now finally and without remedy and he went back to the stern and found the jagged end of the tiller would fit in the slot of the rudder well enough for him to steer... He was past everything now and he sailed the skiff to make his home port as well and as intelligently as he could.
Perhaps, then, if you are looking for an enemy we need to think about the indifferent universe as the biggest opponent of Santiago, as he struggles to make meaning in an immense, impersonal world and refuses to allow his own human spirit to be dwarfed, even by defeat.