Great story that you have here! I think there are some improvements that can be made.
As you stated, I think you should cut down on the elaboration of your story (i.e. the first paragraph can go).
I competed that year at the western Regionals of the World's Scholar's Cup, an international team competition filled with subjects such as Team Debate, Team Essay, Economics, Literature, Fine Arts, etc. I wanted to prove to my coach that he had made a wrong decision - it was the only thing my overconfident, immature 10th grade mind could think of. But looking back at that event, I didn't care that I scored the highest in my school, that I took home more than 10 medals, including 3rd in Team Debate, 2nd overall in test scores, and 3rd overall in the entire competition. I triumphed over my previous loss and gained skills and abilities unattainable at that level anywhere else: speech, debate, problem solving, study strategies, time-efficiency, analyzing, synthesizing, and countless others.
I see that you like to make lists and you've done it thrice in this paragraph (subjects, accolades and skills).
This may send the message to some that you are trying to impress but don't know much about what you are writing. Furthermore, the admissions board has already seen your list of achievements in other sections of your application, so you will be wasting your word count repeating them here in the essay.
It would be better that you cut down on the breadth and focus on depth instead - in other words, perhaps just focus on a couple of things you learnt and elaborate on them. The essay gives you a chance to share about your experiences where you couldn't do so in other parts of the application.
Let's take a look at the question again:Evaluate a significant experience, achievement, risk you have taken, or ethical dilemma you have faced and its impact on you.
This question has two requirements:
1. Share an experience that you have that you feel is significant to you.
2. Share the impact of this experience to you.
You have fulfilled part 1 well, but I feel that part 2 is sorely lacking. The last paragraph is all that it is:
My desire to be the best in these academic competitions had left me with experience vital to life. I went on to fulfill leadership roles in different clubs such as National Honors Society and my school newspaper, I excelled in my classes using the skills I had gained, and most importantly, realized the importance of loss. I recognized that if I learned from my loss, I didn't really lose much at all. Ironically, I gained; "Why didn't I win?" became "What is this loss trying to teach me?" Ironically, my most significant achievement was my greatest loss.
When you are discussing the impact of this experience (in your case, academic competitions), link it more to your personal qualities as well. What is this "experience vital to life" and how has it changed you? Perhaps consider how your opinions, behaviour, interests, attitudes etc have been affected by this. For a start, explain the importance of loss to you?
Honestly, I don't understand the last two sentences of your essay. Perhaps you could explain/rephrase them?
It seems to me that a more apt ending would be: "
Ironically, my greatest loss was my most significant achievement was my greatest loss."
Correct me if I got you wrong here.
Good luck with editing! Btw do give me feedback on my common app essay as well - I selected the same question as you :)