Paulo Coelho's The Alchemist has many differing conflicts going on throughout the story; but, the main one could probably be broken down to the battle between free will and fate. Coelho's fable includes man vs. nature, man vs. self, and man vs. man all into one complete package. First, Santiago must learn to listen to the universe, the earth, the wind, and even the sun in order to become one with nature. Second, Santiago must learn to overcome his own temptations to give up on his personal legend for things like love, weakness, loneliness, or lack of money. Finally, Santiago must take what each person advises him to do with his personal legend and decide whether or not it is for his benefit or not. In the end, Santiago must always make a choice when confronted with a problem or a trial--does he accept fate's decisions, or continue on no matter what obstacles are placed in front of him? By choosing to follow his personal legend with every decision, Santiago comes off the conqueror of self over anything else.
I believe that the main conflict in Paulo Coelho's The Alchemist is Santiago's personal, inner struggle with completing his Personal Legend. That internal man vs. self conflict is constantly bombarded with external man vs. man conflicts, but the main struggle deals with Santiago continually wondering if the journey is worth the trouble. Santiago is met with all manner of obstacles as he travels to Egypt where he thinks a great treasure can be found. Along the way he comes across desert wastelands, marauding bandits, and other life threatening obstacles. He is left beat up and without any money several times. Santiago is left multiple times wondering if he should continue on his journey or if he should just return home.
There's a constant tension within Santiago in which he has to weigh the possibility of finding an actual treasure vs. the treasures and knowledge that he has already gained. That is what I believe the central conflict of the story is.
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.