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.