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She gets really shy around members of the opposite sex.
Literal
She [topic-は] opposite-sex [of-の] front [in/at-では] extremely is-shy.
がる is a productive suffix that turns an inner-feeling adjective (恥ずかしい 'embarrassed/shy') into a verb describing externally observable behavior — 恥ずかしがる reads 'shows signs of being shy.' Japanese is strict about not directly attributing inner states to third parties: you can say 私は恥ずかしい ('I'm embarrassed') but for someone else you typically need 彼女は恥ずかしがっている or 恥ずかしそうだ. The 異性 ('opposite sex') framing is a slightly clinical/formal way to talk about romantic-context shyness.