Prerequisites include Calculus I and the knowledge of basic definition of algebraic numbers. Of course, more experience in or stronger intuition over mathematics always helps.

Although I tried my best to elucidate each step as clearly as possible, I cannot hope to adequately cover every tiny detail in such a lengthy proof. If you have any questions or notice any errors, I would appreciate it if you could comment it below.

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References:
Here is a well-explained proof I found online: http://www.math.utk.edu/~freire/m400s...
I include one more website that also includes the proof that pi is transcendental: http://sixthform.info/maths/files/pit...
*The viewers with more experience may like the less intuitive but more systematic method of relying on taylor expansion in the first website. I used both websites above in the research stage of this video.