Korea & Vietnam may both be in Asia but for the reasons you would like information, they may just as well be as far away from each other, and as different, as Canada and Cambodia. By and large, the governments of most countries insist on a university degree to be able to obtain legal employment as a teacher. A TESOL cert, if needed, is usually a requirement made by the employers, and might not even be needed. However, see my comment below about Korea. Be guided by someone who has first hand experience.
1. Ty Googling teaching job in korea and seeing what it comes up with.
2. Have you thought of simply Googling 'best language school Korea' and seeing what it comes up with?
Generally, the best way to get the better jobs is to be in the country, cold canvass the schools of your choice, and be available for immediate interview if replying to ads. I don't know if this is true for Korea though - I have never been lived, or worked there.