I found top-rope climbing quickly acclimates people to heights, because it repeatedly puts you in situations where you are constantly in high places 5-30 feet off the ground, suspended by ropes, in a situation you're having fun. Having tied all your own knots so that you know they're good, having the ability to ascend gradually and have someone lower you if you get too nervous, having someone below encouraging you and ready to catch you with friction tools ensuring even if you let go of the wall, you just stay suspended at your current height, and getting a better physical sense for one's body as a physical, gravitational object, quickly get you used to being in the air in a context where you're actually having fun, which strongly helps break the fear.

Bouldering, rock climbing on walls without ropes about 5-12 feet in height over thickly-padded floors, accomplishes many of the same goals, and also accustoms and trains you to fall safely and trust in your balance and strength when up high. It's also easier to get started as a beginner, as all you need are rock climbing shoes and a gym.