Schools in South Korea wont hire you unless you have a bachelor's degree. If you want to know what courses to take, then I would suggest as a bare minimum:
- a TESL course, and
- a diploma course
Some lucky teachers have been able to get their visa with only the above, however they have had to prove themselves to the school. The school is not going to jump through hoops for you and get you a visa when they don't even know you and when there is a good supply of university graduates knocking on their door asking for work.
You can always consider teaching in Summer Camps, building up a rapport with the school, and then perhaps converting to a full-time teacher.