Reddit reviews Democracy and Authority in Korea: The Cultural Dimension in Korean Politics (Democracy in Asia)

You may already have a good understanding of 20th century Korea but if not a good place to start is Korea's Twentieth-Century Odyssey. It covers the whole of the 20th century and helps place the democratisation movement in historical context.
As for books focusing specifically on the democratisation movement there is The Politics of Democratisation in Korea and Korea's Democratisation. Those three books should give you a fairly deep understanding but after this you could look at Democracy and Authority in Korea which looks at aspects of Korean democracy such as regionalism etc. The process of democratisation is included in their analysis IIRC. Finally there is Democracy After Democratisation which after a brief overview of the democratisation process it examines the consolidation of democracy in Korea.
I hope this helps somewhat. I can suggest a few journal articles too if you want something immediately to look at.