So while fighting the hydra, I would try attacking the cobalt hydra, but the board would not let me click on its icon. So I tried using an aoe attack, and the attack only hit the heads around the cobalt hydra head.
I was able to complete the dungeon, but there was yet another issue. Once my friend and I defeated Cobalt, Amethyst, and Scarlet, the Ebon came up, but his icon did not appear on the battle board.
As I understand it, there is a bug in this quest that causes the Cobalt Head to appear but not be able to access it on the Battleboard. When this happens, the only way I know of to continue is to flee the combat and start the quest again. Before entering the cave of the Hydra, mark your spot so if you have to flee you can port back to the start of the combat.