I have consistently been "just good enough," living a life of mediocrity with brief glimpses of my ability.
Is this really what you want the central idea of your essay to be?
I know that in most regards this maybe too little or too late and I fully understand the reluctance that may come from viewing my transcripts.
Wow, this is . . . fairly negative. So, you admit you have horrible transcripts and that the university probably should not admit you. Why bother writing the essay at all then.
However, I believe that in order for me to begin on this new path I need a chance. I need a chance to show your institution and myself, the kind of student that I can and will become throughout the rest of my academic career
So? What does your need have to do with anything? What claim does it give you on the university? And what evidence does it provide that you will do anything more with a chance, if given one, than you did with all of the others you admit to having?
This would be a horrible essay even if it was meant to be written as an explanation of your poor academic performance in the past. As it is, it's also off-topic. you haven't said what your academic goals are, or how the program will help you accomplish them. I'd scrap this essay and try again.