I think they have various types of map available at the airport and tourists information centers near the attraction you want to go.
I guess you only want a topographic map for hiking, not for researching, so accuracy is not that important. The Korean government has this weird law where they forbid any detailed map data to be stored on servers outside Korea (technically they are still at war, but didn't they know North Korea have computers that can connect to the South Korean internet too?). As a consequence, Google was unable to provide a quality map in Korea for years. You can use Naver map instead (a big Korean search portal).
Link to map for Jeju
You can see from the above link that they have map for hiking trails (dark green) and elevation lines every 50 meters if you zoom in close enough. If you are not too keen on using a paper map and money is not a problem I would recommend you rent a phone with a data plan after you get off the airport, then download the Naver map app and have this map always with you. Korea is a very connected country and you can expect reception everywhere you go (Yes, islands included)