Alchemical hydra heads are a rare drop from the Alchemical Hydra. It can be combined with a slayer helmet or slayer helmet (i) to create a hydra slayer helmet or hydra slayer helmet (i), respectively. Doing so requires purchasing the ability Use more head for 1,000 slayer reward points.
It can also be mounted in a Skill Hall in a player-owned house. Before it can be mounted, it must be stuffed by the Taxidermist in Canifis, where she will charge 50,000 coins and return stuffed hydra heads to the player. They can then mount the heads using 2 mahogany planks and 2 gold leaves. When players take it to the Taxidermist, she will exclaim "This hydra looks like it might fall to pieces soon. I'll have to be careful to preserve it properly."
Lastly, the heads can be sacrificed to the Dark Altar north of Arceuus, granting 2,500 Prayer experience. This does not require or grant any Arceuus favour.
For an exhaustive list of all known sources for this item, see here