Dark Anima is one of the Dark Aeons and spawns after you have obtained the airship Fahrenheit. Dark Anima can be found at Mt. Gagazet but there are a few steps that you need to take in order to make her appear.
Travel back to the Mt. Gagazet Caves. You can do this by warping to Mt. Gagazet and using the teleportation pads to get you back in to the caves. Head back to the First Trial of Mt. Gagazet, the one where Wakka had to throw his Blitzball at the target, and complete the trial again. This will release Dark Anima at the entrance to Mt. Gagazet near the Ronsos.
Use the teleportation pads to warp yourself back to the Mt. Gagazet entrance.
Each of the Dark Aeons, including Dark Anima, are considered superbosses and are some of the strongest enemies that you can fight in the game. As such, you will need to ensure that your party is fully leveled, has their best weapons and has their stats maximized as much as possible. Refer to the Advanced area of the Tips and Tricks section for additional details.
Also note that Dark Anima has extremely high Evasion which means that she will dodge most of your physical attacks. This can be counteracted by ensuring that your characters have a very high Luck stat, but grinding 
Luck Spheres and 
Fortune Spheres can be a painstakingly long process. High Luck is not required but will make the battle much easier.
Preparing for battle against Dark Anima involves a few extra steps. Make sure that you have at party members that are equipped with the 
Stoneproof or the Ribbon auto-abilities added through customization. You will also need to have Auto-Phoenix and Auto-Protect equipped. Your party members will likely die several times during the course of the battle.
HP: 8,000,000
Elemental Affinities: Immune to all elemental attacks
Immune to Sensor
This will be a long and drawn out battle for a number of reasons: Dark Anima’s Evasion stat is quite high so she will dodge most of your party member’s attacks and her HP is very high.
Her most powerful attack is her Overdrive, Oblivion, which will deal 80,000+ to nearly all of your party members, depending on how lucky you are, typically resulting in an instant kill. Use 
Auto-Life to help your party survive Oblivion or have Yuna summon an Aeon to take the blow.
Having the Ribbon auto-ability equipped to each of your party members will help them survive the numerous status effects that Mega-Graviton will inflict which includes Darkness, Doom, Silence, Sleep and Slow. Doom can pose problems if it happens to impact your party members right before Oblivion, which may not give you enough time to cast Auto-Life.
You can Steal the following items during the battle:
Three Stars (x2) (common)
Elixir (rare)
And Dark Anima will drop the following items when it is defeated:
Dark Matter (common)
Master Sphere (rare)
