Oh well, I can read hangul, and understand basic korean daily conversation... but the handwriting on the scene is quite difficult to read, also it's written on hand lol
so I got curious and searched it on Naver, voila I found the script! I read it and found what Hyesung wrote on her hand is written as footnote!
here's the handwriting,
남운승 경장 총기도난 사건, 합리적인 의심, 형사소송법 325조, 코끼리 퍼즐의 반론, 입증취지, 김기호 할아버지, 지 철수 등등
those are the points they need to counter attack the prosecutor. hope it helps~