To show you’re/your true colors is to show you’re/your true character, feelings, or intentions, as in “You’re/Your cousin seemed laid-back. Then she showed her true colors as a fierce competitor who will do anything to win.”
The idiom comes from the 18th-century nautical world. Back then, ships flew flags to identify their home country. A ship’s flags were known as its colors. Sometimes a ship would trick an enemy into letting it get close by flying the flag of a different country. Just before attacking, the ship would lower the false flag and hoist its true colors. Sneaky!