She was scared of the big earthquake.

Literal

She [topic-は] big [genitive-な] earthquake [object-を] feared.

怖がる (sometimes written 恐がる) is the verb form of 怖い ('scary'), built with the suffix ~がる ('show signs of, exhibit'). The ~がる pattern is the standard way to talk about other people's emotional/sensory states: 嬉しい ('happy') → 嬉しがる ('show happiness'), 寒い ('cold') → 寒がる ('feel cold'), 欲しい ('want') → 欲しがる ('want — observed'). Japanese reserves bare emotion adjectives for first-person introspection; for third-party observation, the ~がる form is used. Object marker を (not に) is normal for 怖がる.