The three words that gives me chills and turn my legs into jelly.
you don't need to put "and" because you've put "that" as a clause.
you can use clause to combine 2 sentences into 1 sentence. so, you may delete "that" or "and".
As I slowly make my way up to the stand, my legs trembled, I stuttered as I spoke, and soon my face became red.
make balance between present tense and past tense.
Public speaking was the challenge I can not defeat.
i think "can not" is a misspelling. the true is "cannot".
After a few mortifying speeches later, I've had enough, it was time I step up and overcome this challenge. I started practicing in my room.
similar correction. balance between past and present tense.
I noticed some of my peers were nervous by their body language
their body languages
I spoked with more confidence; a huge improvement compared to my first speech.
and that the best way to overcome my fear was to face them which enabled me to grow as an individual.
i think "that" is the subject, and "the best way" is the object, so you must put "verb" between them.