FEMINIST is the one word substitute for:

The correct answer is Option (3) → One who works for the good of females

A feminist is a person who supports and works for equal rights and fair treatment of women. The word comes from "feminine" (of women), with "-ist" for a person who follows a belief or cause.
Example: The feminist leader fought for equal pay for women.

Why the Other Options are Incorrect?

Option 1: One who hates females — Incorrect. This is the meaning of misogynist, almost the opposite of a feminist.
Example: The old king was a misogynist who never let women into his court.

Option 2: Fashion diva — Incorrect. A fashion diva is a woman famous for her stylish clothes. Feminism is about rights, not fashion.
Example: The actress is known as a fashion diva for her bold dresses.

Option 4: Female child — Incorrect. A female child is a girl. Feminist describes a person's belief, not a child.
Example: The scheme helps families to educate every female child.