In Path of Exile, the Hydra is one of the four Guardians of the Void. As with The Minotaur, The Hydra has a range of Physical attacks and other means to break you down, though this boss fight swaps out Lightning for Cold Damage attacks, which can both Chill and Freeze you. The Hydra has an assortment of Physical and Cold Damage attacks, many of which can Chill or Freeze. She's immune to Knockback, Poison, Chill, and Freeze.
Barrage: Fires a fast succession of arrows that deal Physical and Cold Damage.
Doom Arrow: Fires an arrow into the air and a progression of explosions occur in a straight line in front of The Hydra, which deal Deadly Physical and Cold Damage.
Fork Arrow: Charges up to fire a single arrow that forks at a set distance to deal Deadly Physical and Cold Damage (300% of base).
Teleport Short: Disappears and summons minions, which drop Cold Damage vortices upon dying before The Hydra reappears at a random location.
Frostbolts: Cold Damage projectiles that continuously fire from the sides of the arena in a random pattern and fire more frequently as The Hydra comes closer to death.
Stock up on flasks with immunity to Freeze and Chill, given her methods of attack that she’ll be coming at you with. One thing you’ll want to avoid is her Fork Arrow once it’s charged, so simply move behind her when this occurs. Stick and move as much as you can and you should be able to take her down without too much trouble.
Make a note of the environment around you, and keep moving will be your best approach. Most importantly, you’ll want to make sure that you close the distance and make the most of melee and ranged attacks in your possession. The further you move away, the harder it's going to be to dodge. She'll stay near to you, turning to fire Doom Arrows and Barrages. When she charges up to fire a Fork Arrow (a blue orb), be sure to move behind The Hydra.
You're going to need flasks with Chill, Freeze Immunity and enough poe orbs, because you can count on being hit by many Frostbolts and attacks from The Hydra. As long as you stay moving and weaving out of the way of Frostbolts, this fight shouldn't be too hard.