University jobs are typically competitive, especially in Seoul. University jobs tend to have lower teaching hours, better pay, and longer vacations than your average hagwon job.
Due to their competitive nature, these days many universities are requiring a masters degree and teaching experience. However, most universities will accept applicants who do not have a masters degree if the applicant has a strong background.
When looking for opportunities, KoreaJobFinder.com has a search feature that allows you to browse only university jobs. However, not all universities advertise their job opportunities on job websites. Most universities have their own websites where they may advertise job opportunities. These positions are often filled by those who take the time and effort to research them.
Since university jobs are often some of the most competitive teaching positions in Korea, it will help to be proactive. Check job boards regularly, and make the effort to look up the English departments for individual universities. Good luck!