。
She ran for her life trying to escape the killer.
Literal
She [topic-は] killer [from-から] try-to-escape, desperately ran.
殺人鬼 ('serial killer, murderer,' literally 'murder-demon') is a heavy compound combining 殺人 ('murder') + 鬼 ('demon, ogre'). The 鬼 dehumanizes the killer in classic Japanese horror-story style. 逃れる ('to escape, flee from') takes から to mark what one is fleeing. The volitional + とする pattern (~ようとする) marks an attempt — '*tried* to escape.' 必死に ('desperately, frantically,' literally 'with the determination of one's death-fate') is a powerful intensifier for actions taken under existential pressure.