Final Fantasy 4 Boss Battle?

I have gotten to the part where I rescue Rosa and the Boss comes with his Dark Dragon and the dragon instant deaths all my characters except the protagonist, then the little girl from earlier shows up and destroys the Boss's dragon with her mist dragon....then he destroys me before I can resurrect and CURA anyone. Plus everytime I attack him he gains life, So I am pretty upset over this part. Whats the secret, and what is the barrier shift the boss keeps casting???