Hello, and welcome to Final Fantasy Answers. What question do you have today?

That could mean two things: How to reach Minerva (the godess) or how to kill her.

To reach: This part is easier. She is fought in mission 9-6-6. Just do all the missions which precede it to reach her (although these missions are difficult in themselves)

To kill: Use materia fusion to max your hp (99999), vit and spr (255) or you will get slaughtered. If you can, you may also want to get your lck to 155 or higher, but this is not neccessary. I strongly recommend Costly punch, as this will always deal 99999 damage to Minerva. Mug or steal are both useful as you can steal 99 phoenix downs from her which should allow you to survive for a LOT longer. Curaga is vital. SP Master (Mastered) is an option as it will null some attacks, but it is not neccessary, and will quickly drain millions of SP. Full Genji armour set is incredibly useful; personally, I wouldn't fight her without it. Make sure you have raise throughout the entire battle, and note that judgement arrow will dispel it. Cure when you need to, doge what you can, and spam costly punch. She has 10 million hp on normal and 20 million on hard so good luck.