"아이가 괴물을 무서워해요."
Translation:The child is afraid of the monster.
무서워요 (무섭다) is a descriptive verb: to be scary. 괴물이 무서워요: The monster is scary. 저는 괴물이 무서워요: As for me, the monster is scary = I am afraid of the monster.
무서워해요 (무서워하다) is an action verb: to be afraid. 아이가 무서워해요: The child is afraid. 아이가 괴물을 무서워해요: The child is afraid of the monster.
Use the action verb for 3rd person subjects.
There are two ways to say "X is afraid of Y".
If X is yourself, you would use the adjective 무섭다 ("to be scary"): X가 Y를 무서워요.
If X is someone else, you would use the verb 무서워하다 ("to be afraid of"): X가 Y를 무서워해요.
Regardless, you would put a topic or subject marker on X and the object marker on Y.