Your first enounter with Anima is in the Macalania Temple after Yuna and Seymour emerge from the chamber of fayth. Seymour uses Anima once you weaken him to about half HP and take out his Guado gaurds.

The first thing you want to do in this battle is protect your characters from elemental attacks. Use one of Rikku's Overdrives and cast a Nul All on your entire party. Or you can have Yuna on haste and cast each individual Nul on your characters, redoing it after they are attacked with each specific element. You will also want to use haste on your characters if its availible.

First, you're going to want to take out the Guado guards. Have Rikku steal a Hi-Potion from each one. This will stop them from using auto poition. From then on its easy, just keep using physical attacks on them with Auro or Kimahri until they are knocked out. Once you're done with this, Seymour will summon the dark aeon, Anima.

Anima isn't that hard in this battle. Quickly go to Yuna's summon list and select ??????. This is a new Aeon that Yuna just got from Macalania Temple, Shiva (one of the most awesome Aeons in the game). Anima will cast Boost on itself and Pain on Shiva, but since she is an Aeon she is unaffected by the status effects and weill only have HP taken off. Quickly cast Blizard and Blizarra on Shiva and keep her HP from going down too quickly, and avoid attacking Anima or it will Overdrive.

Once Shiva's overdrive gauge is full, cast Diamond-Dust on Anima, and it will take off 9999 HP. Keep using the same strategy to Anima quickly and easily.

The rest of the battle is just you defeating Seymour, so keep your characters HP up and cast Bio on Seymour. Also use Kimahri or Auron to cast lots of powerful physical attacks.