Mercurial describes a person who is volatile, quick to change moods, and unpredictable. Level-headed, meaning calm, sensible and steady, is the direct opposite. Ephemerel (ephemeral) means short-lived, laconic means using few words, and skinflint means miserly, none of which opposes mercurial in temperament. So the antonym is level-headed.
Note: The NTA stem does not state whether a synonym or antonym is wanted. Given the options, only level-headed forms a meaningful pair with mercurial, and we have treated it as an antonym question.