It's basically the same animations used for Irene when in battle, but with Annapurna as a battle companion. She's not her pet, but an additional skill she utilizes throughout her adventure with Occavatra. How it works is that Annapurna would backflip out of Irene's backpack and launch 3 spheres at the enemy at Irene's signal. Then Annapurna walks back to Irene to get literally picked up before she gets back inside with the backpack with another backflip. It's not a powerful triple attack, but can deal decent DoT. Annapurna's ability to conjure three lightning spheres stems from her idolizing Warlic. In the quest Xan's Volcanic Fortress, Warlic's prime element is energy as seen when you have him as a guest temporally. It's possible that Annapurna's prime element too, but she might know a few other spells, which she'll demonstrate when she isn't accompanying Irene.