Tran, whatever you do, do not brag about your non-existent English language skills. I hate to say this but if they test you, you will fail. So remove the reference to that in the whole essay. If the reviewer is to base your language skills on this letter alone, he may just send you back to English grammar school. Do not do it. Remove that reference. You will see the reasons why you have to do that as I continue with my review of your letter.
Your first paragraph alone does not make any sense. It does not clearly indicate a purpose, objective and reason for your studies. It is confusing to read and causes a tremendous amount of English comprehension difficulties for the reader. You even use wrong English vocabulary in the paragraph. For example, and this is the worst part of that paragraph, you said:
I have continuously been pursuing my study in Vietnam and when I came to Singapore, I'm well aware of the importance of knowledge particularly as well as the development of the society generally.
There is a verb, there is an adjective, but there is no subject. Importance of knowledge in what? Also, the term is "I became aware of the importance..."
The reasons I'm so into this program are due to the duration of 3-4 years I expect to complete a degree which enables me ample time to have a throughout comprehension.
Duration of 3-4 years of what? Study? Internships? Developing work skills? What? You missed out on the subject again. Also you need thorough comprehension, not throughout. Those are 2 different terms. If you want to use somewhat complex English words, then make sure you at least know the meaning of the term so you can use it properly. Also, your present tense formatting when using verb. You should have said "taking the initiative..." and "doing volunteer..."
These are but some of the reasons why you should not dare the university to test your English language skills. Believe me, you will fail if they do that. The letter alone already tells them you are exaggerating your language skills so you should instead be telling them that you plan to work on your English language skills while you are a student there in order to help you cope with your lessons.