How do you defeat Anima in Final Fantasy XIII?

At the point in the game where you have to fight Anima for the first time, be warned that she's overwhelmingly powerful and her Pain ability causes instant death, or major damage to anyone who is protected from instant death.

Instead just use summons against her. Shiva is a good choice, summons are unaffected by instant death and almost all status conditions apart from Curse, Shiva can also heal herself with Blizzara.