What do you need to teach in Korea?

Is your bachelor's degree worth it? In this case, yes. source

Honestly? Just a bachelor's degree, in any discipline.

Okay, so you also need to be a native English speaker from the USA, Canada, Ireland, New Zealand, Australia, South Africa or the UK. My case was a bit different since I pretty much grew up bilingual (be very, very convincing in that case: build your case with proof that you're more than capable because they will side-eye you if you don't, and may very well pass you over).

Also, you need to have a clean record. I'm not sure exactly how clean but if I remember correctly even a minor car accident could weigh against you.

If you're absolutely sure that you have to go to Korea, then I'd advise you to sign up for a TEFL certification. This will prove that you're serious about teaching. In fact, I'm pretty sure that as of December 2011 it is now a requisite. I mean, they won't turn you away if you have your contract in hand and don't pass the test, but 1) it will earn you a few million Won more if you do pass, and 2) you'll be better prepared than if you just flew over without a clue how to plan a course.