(a) create a four-year-per-term, two-term-limit presidential system like the USA's, and
(b) weaken the power of the presidency in domestic affairs.
As of now, their constitution allows a president to serve only a single five-year term. Korean leaders' increasing unpopularity and seeming ineffectiveness may be due, partly, to being lame-ducks from day one.
Yet, one can understand why the South Koreans established this one-term-limit cap in the 1980s:
(1) 18 Years of General Park: On May 16th, 1961, General Park Chung-Hee staged a coup and soon installed himself in power. In 1979, he was shot dead, ending 18 1/2 years of power. Widely admired today, despite undemocratic rule.
(2) 12 Years of Rhee: Before Park, there was a U.S.-exiled-till-1945, U.S.-sponsored, and rather cartoonishly-cranky old "dictator" named Syngman Rhee, who caused endless headaches for the USA while in power, and who allowed a a bit of kleptocracy to rise up in South Korea. Rhee ruled for 12 years, '48-'60, until he was overthrown in protests.
(3) 8 Years of Another General: After the assassination of General (then President) Park in late '79, his crony General Chun Doo-Hwan soon assumed power. He allowed an election in December 1987, perhaps because South Korea was set to host the Olympics six months later. (Yet another former general in that clique won the election and served a five-year-term through early 1993. [1993-to-Present has seen fully-civilian rule]).