How can I write a 10 minute dramatic monologue for the novel The Alchemist by Paulo Coelho?

Get a pen and a piece of paper and start writing. Don’t worry about what you’re writing, just write. Put yourself in Santiago’s position and write from his point of view. Keep writing until you’re done. That’s your first draft. Then go from there.

You could just pretend you are talking like the character, and talk about his role in the book. Record what you are saying, then write it down.

Do I write like everything is happening to me right at that moment? In other words…present tense?

I would say like you are talking to an audience about your book.

okay…i feel like im merely narrating

I haven’t had whatever guidance your instructor has given you, which presumably would include the definition of “dramatic monologue” that you are supposed to be using. But if I had this assignment for, say, Dorothy in The Wizard of Oz, I might write something that begins like this:

In a single day my life has changed beyond recognition. I awoke this morning and went to school as usual, and my little dog Toto came to meet me after school. On the way home he ran through old Miss Gulch’s garden and chased her cat, and she came straight to our house to complain to Uncle Henry and Auntie Em. To save him from her clutches, there was only one thing to do: I had to run away.

(Et cetera.)

When I read aloud for ten minutes, I am typically reading about 1700 words. I rehearse with a kitchen timer and cut as necessary.

My guess, without actually knowing the discussions your class has been having about the project, would be this:
Summarize the entire story similar to writing a book report. Put the whole thing in first person from the main character’s perspective. Edit it to fit in the 10 minute time frame your allotted, and then just make it sound like the character is reflecting on his life as hes speaking to the audience.