college essay - "how have you overcome a challenge"

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This is quite well-written, both stylistically and grammatically. Your first sentence is a bit too long, though, and should be broken into two or more shorter ones. Also, you might want to discuss in a bit more detail how you went from "hesitant" to "confident" in your social interaction. The transformation is rather abrupt and inexplicable at the moment. Finally, writing with a strong style, as you do, can disguise the problem of over-reliance on weak verbs, but it remains a problem nevertheless:

"Moving from the suburb of Conyers, Georgia to New York City was a difficult transition. As we entered Brooklyn, the crowded streets got my attention. Never in my life had I seen so many people in one city. It was mind-boggling. My parents enrolled me in a private school. This school was completely different from the magnet school I had attended. The students were required to wear uniforms, the teachers were a lot stricter, and, unfortunately, there were no science fairs. On the first day of school, kids gathered in groups to discuss their summer breaks. I was hesitant to join in the conversations"

In this section you rely too much on forms of "to be," though "got" isn't great either. Throughout the rest of the essay, you have many other weak verbs, such as "to have," to make," etc. Try revising your essay with a view to either replacing those weak verbs with stronger ones, or rephrasing sentences to eliminate instances of weak verbs altogether.

For more on using strong verbs, go here: http://www.essayforum.com/general-writing-questions-13/impor tance-choosing-strong-verbs-6143/

I have made the corrections you listed. Please tell me if any more corrections should be made. Thank you!

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Your second draft is even stronger than your first. The only thing that stands out for me is that this

"Moving from the suburb of Conyers, Georgia to New York City proved to be a difficult transition. As we entered Brooklyn, the crowded streets caught my attention. Never in my life had I seen so many people in one city. It was mind-boggling. My parents enrolled me in a private school. This school starkly contrasted with the magnet school I had attended."

is a bit choppy. The sentences are all roughly the same length and use roughly the same structure. Also, logically, it is not clear why the crowded streets made moving a difficult transition, or what it had to do with your parents decision to enroll you in a private school. If you were to revise the essay to make the connections between your ideas in this section stronger, your essay would become even better than it already is.

When I first heard the news that I was moving to Brooklyn, I felt overwhelmed with anger.

I took courses such as AP Calculus, AP US History, and AP Biology and succeeded, by achieving a 5 on the AP Biology test.

My hard work paid off, as I was named class valedictorian of my class, and won many academic, as well as athletic, awards.
I found a home in Brooklyn.

i made the changes you mentioned. do you think this essay is worthy of winning a scholarship? if you could proofread it once more, it would be awesome! thank you so much!! :)

When I first heard the news that I was moving to Brooklyn, I felt overwhelmed with anger. How could I just leave behind my education at a prestigious magnet high school and friends that I had made since elementary school to start all over again? Quite frankly, I had never heard of Brooklyn until a few months before when my mom received a phone call saying that she had gained the position of an internal medicine resident at a hospital in Brooklyn. I begged my mom to let me stay back in Atlanta, but to no avail.
Moving from the suburb of Conyers, Georgia to New York City proved to be a difficult transition. The crowded streets, the diversity of people, and the myriad buildings all appeared so unusual. There were no big lawns or trees or the quiet sidewalks that I was so acclimated to. Instead, the buildings were all packed together. New and unaccustomed to this city, I was daunted by the idea of settling in a town that did not feel like home from any angle.
My parents enrolled me in a private school. This school starkly contrasted with the magnet school I had attended. The students were required to wear uniforms, the teachers were a lot stricter, and, unfortunately, there were no science fairs. On the first day of school, kids gathered in groups to discuss their summer breaks. I hesitated to join in the conversations, afraid of what they would think of me. More than anything, I desperately wanted to succeed in this school and to fit in.
Forced to make the most of what I had in a new surrounding, I grew into a confident girl, seizing every opportunity that came my way. I joined the volleyball team, where I was not only improving my skills, but was also making new friends, and gaining a sense of school spirit. I also became assistant-editor-in-chief of the yearbook staff, where I made friends with a jovial group of kids. I also joined the Math Club and became a freshmen mentor. Once shy and reticent, I was now letting go of the diffidence in me. A sophomore, I did not hesitate to converse with upperclassmen at club meetings and at volleyball practice. Slowly, I realized that the kids at my school were very affable and helpful.
When I first moved to Brooklyn, I was afraid that my new school would not offer me the same caliber of education as the magnet high school I had attended in Conyers. To be sure that I was not compromising my education, I took the most rigorous courses that my school offered. I took courses such as AP Calculus, AP US History, and AP Biology and succeeded, achieving a 5 on the AP Biology test. My hard work paid off, as I was named class valedictorian, and won many academic, as well as athletic, awards.
I found a home in Brooklyn. I realized that there were so many things to do here; probably more so than in Conyers. I enjoyed taking trips to Manhattan on the weekends and walking through Central Park.
My transformation from a timid, naïve girl to a confident and mature individual is proof that I overcame the challenges that stood in my way. I was able to adapt to a different environment and maximize every opportunity I was given. My experience has enabled me to embrace change and use it as an opportunity to grow into a stronger person.

Omit "Quite frankly," as these are empty words.

"I joined the volleyball team, where I was not only improved my skills, but was also made new friends and gained a sense of school spirit."

It's hard to say whether you can win a scholarship with this essay. So much depends on what they are looking for. The adversity you overcame was difficult for you but is relatively minor in relation to the adversities other applicants might write about. All of which is to say, if you don't get the scholarship, it might simply be that they were looking for somebody who had faced more adversity rather than because of the quality of your writing, which is lively and competent.

It depends upon the criteria used to select scholarship recipients. If they are looking for someone who has accomplished a lot academically, and who has a solid mastery of the English language, then you are in good shape. But not all scholarships are given to reward academic merit -- some are destined for students with great financial need, or students who demonstrate particular commitment to community service, or to some specific political cause. There is nothing in your essay that would particularly qualify you for these sorts of scholarships. I am guessing though, that this is an application for scholarships in general, rather than for a specific scholarship. If this is the case, then at least some of the scholarships you are competing for should be based on criteria you clearly meet, giving you a decent chance, at least.