The Japanese were successful in their invasion on land, taking all of present day South Korea OUTSIDE of the Honam region (present day Jeolla-do, the south-west third of the country) and as far north as Pyongyang. A combined force of Koreans and Ming Chinese were able to stop them there and begin a very serious war.

The Japanese plan was the re-supply their forces via ships. This is where Yi Sun-shin comes in. His naval force was able to sink the re-supply ships being sent around the south-western part of the peninsula, as well as attacking the Japanese fleet piecemeal in the harbors around the south coast. Out of supplies, the Japanese began negotiations with the Ming.

During the second part of the war, Yi was able to catch a few of the Japanese fleets off-guard and crush them. During one of these battles, Yi was shot and killed, ala Horatio Nelson a few hundred years before such a thing was popular. During that battle (Noryang Point), over half of the Japanese fleet was destroyed. The Japanese leader, toyotomi hideyoshi, had died a few months earlier, the new Japanese leaders were ending the war, and that was the end.

So, does Yi Sun-shin deserve the credit? Yes. Two of the four naval commanders in the south coast area burned their ships and ran off. Yi, almost singlehandedly, prevented the Japanese from re-supplying their armies in Hanseong (Seoul) and Pyongyang, and using a combination of hit and run tactics (on the harbors) and being an outright better commander on the open seas, he destroyed the Japanese navies at something like a 3:1 or 4:1 ratio.