To beat the hydra with psych, you need electrical storm fully upgraded, traumatize 2/2 (and twice on your action bar), dark echoes 3/4(once on action bar, insecurity 1/3 (once) and wraith form. Traumatize the hydra, turn to wraith, use insecurity, then traumatize, then dark echoes, then corruption. Then use the electrical storm on the fire claws, it kills them quickly (or at least it did for me) and also have terrify 4/4 on your action bar once. Use terrify as necessary to stay alive and between the other attacks.
Here's the full list of achievements: hobbits = read instructions/credits. dwarves = reload the game 3 times. bombermen = lose 3 times. angels = upgrade everything for all 3 races (humans orcs elves). red dragons = defeated level 17. devils = defeated level 18
 "Thing-Thing Arena 2"){kind=icon}
 "Sonny 2"){kind=icon}
 "Epic War 2"){kind=icon}
 "Amorphous+"){kind=icon}