Which member of the akatsuki was killed in chapter 363 and how?

Deidara.

Deidara cursed the Sharingan, as well as Itachi and Sasuke, and made one last attempt to defeat the Uchiha by using C0 to blow himself up. The attempt failed, as Sasuke summoned Manda to protect himself, at the cost of Manda's life, leaving Deidara's death to be in vain.