Cocatrice are brown hens with a red crest.
They're most commonly found in the first section of the forest, but can also show up on the second area too. They will appear in groups of 2 or 3.
After being assigned by the Hunter in the Slums to hunt Cocatrice, they will drop a diamond ring to finish the quest.
(will update later)
One of the quests that the Hunter will give you (he's in the second door to the left past the merchant in the slums, right before leaving the slums area) is to hunt Cocatrices for a diamond ring that they stole. The diamond ring generally spawns after killing the first Cocatrice, but if not keep killing them until you get it. The Hunter will award you 750 gold for completing the quest.