You come across as being super desperate at the moment.
This comment is not meant to be an insult. Its just that people generally make terrible decisions when faced with desperation.

Not getting into NUS Law does not equate to an academic failing. Many successful lawyers and in house counsels and professors have graduated from universities other than NUS Law. There is even a judge who graduated from Flinders - i didn't even know such a university existed until i appeared before said judge and googled him. Our civil procedure practitioners books are written by a graduate from nottingham university.

My point being. You are not yet at death's door. You still have a year to get a training contract - it is not too late to make a decision as to your future at that time. Focus on sending out applications for TCs. Send out a few everyday. Send out to every single law firm you can find on google - it's what i did. Be tenacious. Be persistent.

Do not be desperate.

A masters is not worth it. Don't waste your parents hard earned money on another year of no guarantees.