As Danzō and his men surrounded Shisui to take the left eye, Shisui managed to escape. ... The contents of the suicide note also made it appear as though he had crushed his eyes when jumping off a cliff into the Naka River to kill himself in order to prevent conflict from arising over his eyes within the clan.

When did Itachi kill Shisui himself?

At the time Shisui died, he was 16 and Itachi was 12-13 years old.

What episode does it show Shisui kill himself?

"Shisui's Request" (シスイの依頼, Shisui no Irai) is episode 454 of the Naruto: Shippūden anime.