"My greatest achievement in life is undoubtedly my greatest failures in life." Choose either singular or plural, greatest achievements are greatest failures or greatest achievement is greatest failure.
You can't say "I, unlike others" because it's assuming others haven't learned from their mistakes
I'ts generally not a good idea to use "you" in an essay
The idea is there and you make some really good points, but the fact that you don't reveal anything about your personal mistakes and what you got out of them makes it a very generic essay. It doesn't tell the reader anything about you. The essay is about you, so don't write about humans in general or how it's normal for everyone to make mistakes. Write about why you are different and how those mistakes have made you learn things others maybe haven't, or things in general that will make you stand out.