Initial requirements before one attempts to fight Alchemical Hydra (non-wilderness):
Like a Boss perk which is a reward that is bought
For 200 slayer points in the slayer reward shop.
To mitigate this, one can get a regular slayer task of hydra's,
Which the boss is applicable with this task.
95 slayer, a slayer task, and at least 43 prayer are all necessary;
At least 70 range, and 70 defence are highly recommended.
Boots of brimstone or boots of stone are not a requirement
As long as you have completed the Kourend and Kebos hard diaries,
Which give you the ability to wear any boots, such as pegasian's, devout's, god d'hide, etc.
Miscellaneous suggestions: "Too much boss" relic (like a boss is a requirement)
That is bought with bonds, giving one the ability
To be assigned a boss task as much as one would like.
The tile/ground marker plugin is a very helpful tool that
Can be utilized in order to mark out each pathway for each Geyser and where to stand
In relation to Hydra itself, making this ideal for someone first starting the boss.
Shift + right click is how to mark the tiles that one wants to place.
If one has donator rank, the red portal at ::dz can be used
So one can teleport directly in front of the boss room.

Now, before we get to the gear, I shall discuss this boss's mechanics in a very thorough manner.

Attached underneath is a video of me going through the boss fight itself,
Which will help guide one with more precision
In conjunction with the explanations I am about to convey.

First Phase -

When one first enters the boss room, run to the farthest end of the north-east side of the room,
Just on the other side of the Red Geyser. Be prepared to pray either range or mage while you are running.
Alchemical Hydra's first phase will either fire a projectile that is spear shaped (range)
Or a blast that is a combination of 3 line like projectiles (mage).
The main goal, besides surviving and killing Hydra, is to get Hydra to place itself
On these 3 Geysers that correspond to the 3 different phases of Hydra; this decreases Hydra's defence drastically, which is very very helpful.
Though Hydra has 4 phases, this last one will be spoken of...well last.
To continue from the projectiles, whichever projectile this may be, it will always be done in a combination of 3's,
So with every 3rd projectile that hits you, say if it was range, change your prayer to mage.
On this first phase, after the first 3 projectiles, Alchemical Hydra will throw out spats of poison
Towards you that stick to the floor for a short duration. If you are hit by these, they do 12 damage each so it is highly suggested to avoid them.
If one is to walk over one or is to be hit by one, they will become poisoned (antidote ++ or anti-poison is recommended).
After this has occurred, whichever projectile that Hydra had ended with after the poison will not be what is projected next, it will be the other one.

Second Phase -

When Hydra is depleted to 75% health, this is when a head will detach from its body, falling to the ground, and Hydra will morph into a blue color.
During the process of this happening, run to the north end of the room, right past the Green Geyser
(whichever projectile hydra ended with when it morphed, is not the projectile that hydra will fire).
Everything besides the poison occurs in the same manner; Hydra will now instead spawn blue lightening
That traverses throughout the room and you are the center of their attention,
They want to give you a hug, do your best to not allow them to give you a hug.
I have found that when hit by them, they tend to disappear, so I'd almost say, give them a hug if you'd like (they do little damage).
Now, my recommendation is when Hydra hits roughly 60% (it can be lower) run to the far west side of the room, right past the Blue Geyser.
Doing this will allow you to get more hits on Hydra's next phase, which is now a perfect time to introduce Hydra's rage phase.

Third Phase -

When Hydra reaches 50% health, another head of Hydra's will fall to the ground, and now Hydra will morph into a red color.
If you do not follow my recommendation, that is fine, proceed to take hydra to the far west side of the room where the Blue Geyser resides.
Whichever projectile Hydra ended with on the previous phase is not the projectile Hydra will use.
After Hydra has fired 3 projectiles, Hydra will walk to the center of the room and unleash 2 rectangles of fire, one to the side and one in front of itself.
If you are in a corner, you can easily avoid these. After this, Hydra will immediately fire a heat-seeking flame that follows you
So you must run in order to avoid this (it lasts for about 15 seconds...give or take).

Fourth Phase -

After all of this has occurred, everything begins to become easier, for when Hydra reaches 25%,
This is when the last phase commences. Whichever projectile Hydra ended with in the previous phase,
Hydra will use the opposite of at the beginning of this next phase.
Hydra will lose another head and morph into this light coal like color,
Where Hydra's defence will slightly increase, (no geyser works to decrease it)
But this phase is synonymous with a Jad Phase,
Meaning Hydra will fire a projectile one time, say range, and the next projectile will be mage, so on and so forth.
After Hydra has fired 3 projectiles, it will cast out some poison again.
Whichever projectile hydra used before it casted out the poison, it will use the opposite one afterwards.
Hydra at this point has clearly had enough while you on the other hand are very close to killing it.
Continue with the method described in the explanation or showcased in the video and hydra will finally drop dead.

Gear Selection -

Gear selection varies quite a bit. I will give 5 different setups that are generalized (the fifth is my own) along with the inventory loadout.
All of the gear itself that is listed (or not listed) can, for the most part, all be interchangeable.
Dependent upon your own gear availability, you can create your setup however you'd like, as long as it is effective,
For this is just a general list of all of the gear I recommend, ranging from best in slot to the least effective that can still be effectively utilized.
I realize that I do not have the best in slot gear for on task
With images but I will list it out nonetheless. Also, full Karil's with an Amulet of the Damned full is a viable gear setup.

Best in Slot Gear -
Slayer Helmet (I), Necklace of Anguish, Ava's Assembler, Armadyl Chestplate, Armadyl Chainskirt
Twisted Bow with Dragon Arrows, Boots of Brimstone, Archer's Ring (I) Or Ring of Suffering (I)

setups and loadout.jpg

First setup is the lowest effective gear setup that is recommended.

Helm Slot: Slayer Helm (I)
Necklace Slot: Amulet of Fury
Torso Slot: Black D'hide Body
Legs Slot: Black D'hide Chaps
Boots Slot: Boots of Stone
Backpack Slot: Ava's Accumlator
Right Hand Slot: Magic Short-bow (I)
Left Hand Slot:
Arrow Slot: Amethyst Arrows
Gloves Slot: Barrows Gloves
Ring Slot: Archer's Ring (I)

Second setup -

Helm Slot: Slayer Helmet (I)
Necklace Slot: Amulet of Fury
Torso Slot: Zamorak D'hide Body
Legs Slot: Zamorak D'hide Chaps
Boots Slot: Boots of Stone
Backpack Slot: Ava's Accumulator
Right Hand Slot: Armadyl Crossbow
Left Hand Slot: Book of Law
Arrow Slot: Ruby Bolts (E)
Gloves Slot: Zamorak D'hide Vamb Braces
Ring Slot: Archer's Ring (I)

Third Setup -

Helm Slot: Void Range Helm
Necklace Slot: Amulet of Fury
Torso Slot: Void Knight Top
Legs Slot: Void Knight Bottom
Boots Slot: Boots of Stone
Backpack Slot: Ava's Assembler
Right Hand Slot: Toxic Blow-Pipe
Left Hand Slot:
Arrow Slot: Zamorak Blessing
Gloves Slot: Void Knight Gloves
Ring Slot: Archer's Ring (I)

Fourth Setup -

Helm Slot: Crystal Helm
Necklace Slot: Amulet of Fury
Torso Slot: Crystal Body
Legs Slot: Crystal Legs
Boots Slot: Boots of Stone
Backpack Slot: Ava's Assembler
Right Hand Slot: Bow of Faerdhinen
Left Hand Slot:
Arrow Slot: Zamorak Blessing
Gloves Slot: Zamorak Vamb Braces
Ring Slot: Archer's Ring

Fifth Setup is my own

Inventory Loadout...Which can be modified in any way that one desires -

4 Prayer potions
1 Antidote ++
1 Range potion
17 Angler Fish
3 Karambwans