Use the adjective unfazed for someone who's not disturbed or frightened. You might squirm in your seat and cover your eyes during the scary parts of a movie, while your little sister is completely unfazed.
If something doesn't faze, or disturb you, you're unfazed. All of your friends might shriek and run away when a giant spider lands on the sofa beside you, but as a budding arachnologist, you remain unfazed. A common misspelling is "unphased," which isn't a real word. Faze and unfazed are American English words thought to derive from the 15th-century Kentish feeze, "frighten."