How can my Volcarona learn Giga Drain in Pokémon Y?
Volcarona can't learn Giga Drain in Pokémon X and Y. Volcarona could only learn Giga Drain through the Move Tutor in Pokémon Black and White 2.
So the only way to get a Volcarona with Giga Drain in your game is if you get a Volcarona on Pokémon Black 2 or White 2 teach it Giga Drain and transfer it to Pokémon X or Y using Pokémon Bank, or if you miraculously get one through trade.
Hope I helped :)
Volcarona can only be obtained from Gen 5. Without the use of Pokebank, there is no way to obtain a Volcorona with Giga Drain in Pokemon X or Y