How to get the invocation of Shiva
There have been so many different summons over the years, but there are always a few staples. Shiva is definitely one of them as an ice-based summon that you can acquire in the first half of the game.
Specifically, you will first have the chance to acquire Shiva from Chapter 8, when Chadley informs you about his new VR Combat Simulator. This allows Cloud to put on a VR headset and face a powerful summon, with Shiva being the first. There is more you can get on the line, but Shiva is the only one you can tackle at this point.
As you can guess from the movements of the Ice Type, Shiva's weakness is definitely going to be Fire. This means you'll want to try and use as much Fire as possible between Cloud and Aerith, or whoever you have in your party if you don't do that until later in the game.
Another major key to winning here is using one of your other summons, Ifrit. Ifrit is the classic fire-based summon, so he will be able to deal massive damage to Shiva, especially if you use his special summon abilities.
Try to dodge Shiva's most powerful attacks and keep attacking him with Cloud and using Aerith's Fire spells in particular. Hope you have some higher level Fire spells at this point as Fira can be of great help. Firaga is probably not worth the cost or the time to throw at this point, so I would stick with Fira at most here.
Eventually you will bring down Shiva and will be rewarded with Chadley's Summon of Shiva Materia as soon as you are done.
