Is there anywhere where I could find a translated text of it? I can never find it, maybe I'm not looking in the right place.
An English translation was published as Nanjung Ilgi: War Diary of Admiral Yi Sun-sin by Yonsei University Press in Seoul in 1977.
It's not too easy to find affordable copies second hand (in fact, wow, maybe I should sell my copy), but it ought to be in larger academic and specialist libraries.