There's a long story behind why, but in FFX a Summon Beasts' true form is a person who died and became something called a Fayth. The woman who became Shiva's Fayth is a brown haired woman with colorful heavy winter clothing and you can hear her (soprano) singing Song of Prayer at Macalania Temple.

Every part of the temple is decorated or marked with symbols for Yevon and Ice. You actually acquire Shiva at this Temple before doing the Hall of Trials. According to legend it's because of Shiva that the area around her temple is always frozen no matter what time of year.

You should use Shiva during the battle against Seymour's Anima. Shiva will show up as ?????? in Yuna's Summons menu. Stick to using Blizzara (because it wont make Anima's OD gauge rise as fast as attacks do), heal yourself with Blizzard spells and use her Diamond Dust when her OD gauge is full.

After this battle you will still end up having to do the Hall of Trials on the way out of the temple. This Hall of Trials is pretty simple, if you need help check out gamefaqs.com. Be sure to revisit the Fayth room in this temple later on for treasures and to learn about this Fayth's history. In fact, in the International versions you can also battle against Shiva (not the same as the ending sequence).

This is the most complicated and detailed Shiva yet! From her wicked intro with her liquid ice form materializing to her winpose, to her sassy overdrive she just rules! This 7ft tall ice momma is always tough and even as she is defeated in battle, she's just barely kneeling as though she doesn't want to give up.

In keeping with the 'rainbow' theme of Spira, Shiva's design has every color. She has lots of jewellry in it too. She also has a mysterious thing hanging from her left arm which all summons happen to have. Also with the game's theme of imbalanced designs, Shiva is pretty much different on her right and left halves of clothing and skin. In her intro, Shiva also tosses off an ice cloak to Yuna (which disappears again oddly), the cloth has some Indian-style print on it. Lots of ropes and anchors are also all over Shiva's hair and hanging from her waist.

You can see Shiva's Fayth form on the floor in Macalania Temple's room of the Fayth. Sealed in the glass is an impressive darkskinned topless woman (with an x across her back) facing the ground. Her hair is like Shiva's but dark and spread out, and she seems to be like a mermaid. The anchor around Shiva's waist and bangle-decoration (a protective equipment like Lulu's and Yuna's I think) is also there but slightly different.

Default Commands

Fight	(Tatakau) Shiva does a low gravity looking drop kick for physical damage (raise Shiva's Physical Strength stat for more damage). The Attack Power is 14 and does less damage on enemies with Protect casted. You can get Critical hits on this and Shiva looses 3 on her Speed stats until the next turn.
Heavenly Strike	(Tenkara no Ichigeki) Shiva makes a block of ice fall onto the opponent from the heavens. The Attack Power is 17 and it does physical (not Ice Magic) damage and has a 100% chance of causing Odosu (Threaten aka Stop) on the opponent if the opponent is not guarded from it, it also slows down the enemy. Use this to hit an enemy that's anywhere on the screen and you can't reach with normal attacks. It cannot be Reflected but does less damage on enemies with Protect casted. You can get Critical hits on this and Shiva looses 4 on her Speed stats until the next turn.
Black Magic	(Kuro Mahou) Use any Black Magic spell Shiva has learnt. Blizzard spells heal her. By default Shiva has Blizzard [4MP] and Blizzara [8MP].
White Magic	(Shiro Mahou) Use any White Magic spell Shiva has learnt. By default Shiva has BaFire [2MP] and BaCold [2MP].
~ Diamond Dust	Shiva's overdrive available when her gauge is full. She kisses the air to freeze it, then sends a powerful blast of ice freezing the enemies. She then snaps her finger as the ice breaks, damaging all enemies. The Attack Power is 60 and this does Ice damage (Magic damage - raise Shiva's Magic stat for more damage), cannot be reflected and there's no critical hit versions. Shiva looses 8 on her Speed stats until the next turn.
~ Defend	(Mamoru) Shiva casts protect on herself and defends. All incoming attacks take off very little but her OD gauge doesn't rise much. Use this when the monster's turn is coming up and its OD gauge is full.
~ Store	(Tameru) Shiva lowers her defense while sparks burst around her and she absorbs any attack. All incoming attacks take off more damage but her OD gauge rises quickly. Use this on weaker enemies.
~ Return	(Modosu) Shiva jumps out of the screen and the normal party resumes battling.

Initial Statistics
Hit Points: 820 (1x normal)
Physical Strength: 19 (1x normal)
Physical Defense: 17 (1x normal)
Speed: 14 (3x normal)
Hit: 20 (1x normal)
Magic Points: 26 (2x normal)
Magical Strength: 23 (2x normal)
Magical Defense: 24 (2x normal)
Evade: 32 (3x normal)
Luck: 11 (1x normal)

Normal & Short Animation
Use the option in the Menu - Config screen to toggle normal and short animations. Shiva's shortened animations are her intro and Diamond Dust overdrive. The intro skips to where she appears and throws her cloth to Yuna, and Diamond Dust skips to where she snaps her fingers. Her physical and magical attacks/use are the same animation though.

No matter what your setting, the first time you summon Shiva and the first time you use Diamond Dust, you get the full animation. You also get her full intro animation in the final battles against your summons (where she's purple). As a side note, her magical attack animation is very similar to Rinoa's motion in FF8.

Learn - Teaching Commands
You can use various items to teach Shiva new spells and abilities in the Summons - Learn sub menu. She has quite a few by default. I personally didn't bother with this since it costs a lot of items and I never would need to use it aside from maybe Blizzaga for healing myself (when Blizzara doesn't heal enough) or ReRaise for in case Shiva runs outta HP. Keep in mind Shiva absorbs Ice attacks on her, so casting BaCold is never necessary.

Educate - Raising Stats
There's various ways to raise status. By default Shiva grows as Yuna grows, but by a fraction. For every 1000HP Yuna gains, Shiva gains 460. For every 100MP Yuna gains, Shiva gains 9. When Yuna's Physical Strength goes up by 10, Shiva's goes up by about 14. When Yuna's Physical Defense goes up by 10, Shiva's goes up by about 6 and so on.

The other way to raise stats is by using up items with the Summons - Educate menu. These usually take up A LOT of spheres and are rarely worth it. If anything is really needed and you have spheres and items to blow, just power up Shiva's HP or Speed (which btw is already pretty good for a mid-level Summon). You do have a limit as to how many times you can do this and you can't up Luck stats.

Exceed Max Damage
Acquire Lulu's Knight of Onion (aka Onion Kid) final weapon from the underwater circle area near the Baaj Temple. No need to have it equipped nor powered up, Shiva will then be able to do more than 9999 damage to enemies.

Changes
Shoukan Kedamono this time becomes Aeon. Aeon actually means a long period of time. This could have to do with the Fayths summoning and dreaming for 1000 years.

Dark Shiva
Statistics
HP: 1100000
AP: 20000 (overkill 30000)
Physical Strength: 173
Physical Defense: 163
Accuracy: 250
Magic Strength: 244
Magic Defense: 255
Agility: 255
Luck: 73
Drop: Dark Matter, Master Sphere

Battle
Before the battle, everyone must have Auto Phoenix, just about everything of hers is an instant kill becuase she exceeds max damage. Max Aeons' overdrives and use them as shields from her own overdrive. A typical Dark Aeon fight, you will need to have high agility to dodge her attack, and accuracy to hit her. Beware using magic, Ice is absorbed, Lightning/Water is nulled, Fire damage is halved.

Shiva's Speech to Tidus
"Should the dreaming end, you too will disappear -- Fade into Spira's sea, Spira's sky. But do not weep, nor rise in anger. Even we were once human. That is why we must dream. Let us summon a sea in a new dream world. A new sea for you to swim."

Final Fantasy X-2
Dark Shiva makes a small appearance in this game where summons no longer 'exist'. She can be optionally battled in the Farplane.

Gallery