I don't want to go line by line (I don't have the time this morning, sorry), but you should break down your essay into three or four sentence-long chunks. This is whether they are related or not, by the way.
Look at each of your sentences and search for redundancies, either within a sentence or from sentence to sentence. Start cutting, and be ruthless.
For example, you write,
I no longer want people to see a little dot on the map when they think about the Cayman Islands, but a face they remember from an excellent ambassador of the Cayman Islands representing the culture and traditions, named Derricka. I’m confident that after two years of studying at UWC I will be able to use not only what I have gained to cultivate myself and the Cayman Islands, but the world.
Instead, cut the hell out of that fatty combination of sentences, to come up with something more like this -
After two years of studying at UWC I am confident I will be able to use what I have gained to cultivate myself, the Cayman Islands, and the world.
Once you have cut within your chunks, put them together into larger chunks and see how the whole thing flows.
If you're under 300 words, start tackling the description of your background, etc. If you aren't, then seriously consider scrapping the entire essay in favor of only answering the parts you were unable to get to, and then see what you can add of your preexisting work.
But go through the editing exercise first. See where you are repeating yourself or are padding. Hint: you are padding a lot.