Just like in the resume, you’ll want to emphasize your most marketable traits first.
You’ll also probably need to include a paragraph about why you want to go to Korea. It’s ok if you don’t know much about Korea, but try to express an earnest curiosity an willingness to accept a foreign culture. If you’ve ever lived abroad (or even traveled extensively) this would be a good chance to mention it. It will help employers recognize you as somebody who is capable of adapting to life abroad and will not suffer from major culture shock.
As far as tone goes, you want to sound intelligent but keep it simple. Remember that the person in charge may not speak English. However, a native speaker will probably read your application at some point in the process. To strike an appropriate balance, you should be articulate, throw in buzz words, and proof read carefully, but try to avoid philosophical digressions or flowery prose.