For this achievement you have a choice. You can choose to defeat the Hydra or the Archydra.
Defeating the Hydra:
The Hydra can be found in the Frontier Caverns after you accept the notice board quest "A Challenge" in Cassardis during post game. The Frontier Caverns is that place accessed through The Shadow Fort. Here is a map to help.
Go here for tactics and other information about the Hydra.
Defeating the Archydra:
The Archydra can only be found in the Chamber of Hesitation in the Everfall.
Go here for tactics and other information about the Archydra.