The only issue with the answer above is that it fails to fully explain the main conflict by mentioning all four. I will attest, then, that the main conflict is that of fate vs. will. Now let's look at how this one main conflict is reflected in each of the elements of the story.
First, Santiago has to contend with the earth and the solar system. Is it his fate to become one with nature? Or is it Santiago's choice? I would suggest the latter, therefore, Santiago wills it so in order to pursue his legend and legacy. Next, Santiago struggles with temptations. Is he fated to lack love? Be weak? Be lonely? Be poor? No. Due to Santiago's own decisions, Santiago overcomes each negative trait.
There is only one thing that makes a dream impossible to achieve: the fear of failure.
Third, Santiago comes across different people who give different advice. Is it Santiago's fate to follow each one? No. Santiago listens intently to each and then makes the best choice according to his own will.
In these three ways, Santiago becomes the hero of the story. In the conflict of fate vs. free will, Santiago chooses free will. It is this choice that helps him triumph over fate.