Yuna is given an opportunity to fight against Shiva at the Calm Lands in an aeon battle with Belgemine. The player must beat Shiva and all of Belgemine's aeons in order to receive the Aeons Soul item that will enable aeon development. The player will also receive 30 Power Spheres. Every other battle won against her will earn 30 Speed Spheres. Furthermore, the player needs to beat Belgemine at Remiem Temple to obtain the Moon Sigil, in conjunction with 60 Mega-Potions. Every other battle won will earn the player 6 Star Curtains.
In the first battle, the opposing Shiva has 15,000 HP and 900 MP. She absorbs any ice attacks, all status ailments and any break attacks, such as Power Break. Her weakness is fire based attacks.
At the Remiem Temple battle she has 20,000 HP and 950 MP. Her immunities, weaknesses and absorptions are the same.
Yuna also encounters Shiva as an enemy inside Sin. Shiva's stats are identical to that of when being summoned by Yuna.
A simple strategy is to summon Ifrit with the Overdrive gauge fully charged. This will put an immediate strain on Shiva's HP and even more so if Ifrit has unlocked Break Damage Limit. Shiva can also damage Ifrit severely, but this can be solved by Ifrit casting a fire-based spell on himself, or using NulFrost to cancel out ice attacks. Summoning Bahamut is also an easy way to win this fight, as Shiva will do minimal damage on him and Bahamut can cast Firaga. Bahamut can already break the damage limit, and Mega Flare should be an Overkill.
In the battle within Sin, a good method is to use Lulu, Yuna, and Auron (or any of the other male characters; Rikku won't be of much use unless she has Fire Gems). Yuna should heal and cast NulFrost, Lulu attack with any of the fire spells and using Reflex, and Auron should use Armor, Magic, and Mental Breaks on her.