The Hydra's element is Fire/Water so it is weak against Water/Air and it is strong against Spirit/Fire. You can face it in the Normal stage of Blazing Tides or at the Summoning Stone. If you beat it 10 times, you will get the achievement Head Hunter. It drops Hydra Scales which can be used to craft Hydra Hunter's Mail or Crimson Scales which can be used to craft Dragonflame Armor.