Attunement to the Core is obtained by speaking to the blood elf Lothos Riftwaker outside of Blackrock Depths. It is strongly advised to complete this quest since, once completed, Lothos Riftwaker can teleport you directly inside, bypassing BRD entirely.
The [Core Fragment] you are asked to obtain is just outside the entrance to Molten Core inside the Blackrock Depths instance.
Hydraxian Waterlords is the faction opposing the forces of Molten Core. There is a quest chain off the coast of Azshara (79.73). It starts off with Duke Hydraxis providing you with 2 quests:
Quest 1 - Poisoned Water: Kill water elementals in EPL
Quest 2 - Stormers and Rumblers: Kill wind and rock elementals in Silithus
Once this is done, visit the Duke a second time and they will have a third quest:
Quest 3 - Eye of the Emberseer: Collect the Eye of the Emberseer from Pyroguard Emberseer. The first main boss in UBRS. This CAN be done in a raid.
Return to the Duke and he will give you quest number four:
Quest 4 – The Molten Core: Kill one Ancient Core Hound, one Molten Giant, one Firelord, and one Lava Surger. Easy enough to do on an MC raid.
Once this quest is done the Duke will give you a quest to reach Honored with the Hydraxian Waterlords faction. Elementals in Silithus, the Burning Steppes, and everything in MC will give
reputation.
Once Honored, the Duke will give you quest number six:
Quest 6 – Hands of the Enemy: Collect the Hands of Shazzrah, Lucifron, Gehennas, and Sulfuron.
Quset 7 - A Hero's Reward
Once the player reached Revered, Duke Hydraxis offered a self-replenishing [Aqual Quintessence] to douse the runes of Molten Core.