This may very well be the most epic struggle you ever have. Shooting down that great Black Dragon is no easy feat, and will require the greatest of preparation and perseverance.

If you do not know how or where to get something listed below, or you do not quite meet one of the stat requirements, then you are probably not ready for this challenge. Sorry, but really, I am saving you from unnecessary frustration.

Progress
Have defeated Kalameet before (and gained Hawkeye Gough's Greatbow)
NG+ or higher
Able to fight Kalameet (obviously)
Estus reinforced to +7 (from 7 Fire Keeper Souls, so need NG+ at least)
Rite of Kindling, kindle Oolacile Township bonfire to 20 Estus Flasks

Stats
High Vitality, the higher the better (recommended 50)
Maximum Stamina, 80 equip burden (40 Endurance satisfies both)
50 Strength (for Havel's Greatshield)
20 Dexterity (higher for more damage, recommended 40, the more the better)
100,000 spare souls (one-hundred thousand) for buying the arrows

Gear
Iron Tarkus armour set
Havel the Rock Greatshield
Either Gough's Greatbow (recommended) or Dragonslayer Greatbow
At least 100 arrows, recommended number 150
Hawk Ring
Another ring to benefit you, I used Ring of Favour and Protection, though the Leo Ring could probably work better

Time
One whole hour to spare (go to the bathroom first!)
The patience of a Primordial Serpent

Please note that the Silver Talisman does not deflect Kalameet's fire. Evidence below, or go to https://www.youtube.com/watch?v=hTy8Q24XW2o. Excuse the poor fashion sense. Note that I am not claiming anything about during the actual (ground) boss fight with Kalameet.

Meeting all the requirements, and ready to fight an epic (that means long) battle, rest at Oolacile Township bonfire, then head to Kalameet's boss room.

I recommend practising first: Accept that you will die, do a few trial runs of the below methodology: Get to the right place, practise block timing, practise shot timing, practise aiming. Push forwards from the recommended standing point to see how far you can go. This is a good time to check that you can take a hit from Kalameet's fire without dying (hit without shield, even better can survive hit after shield is thrown back, during instability). When satisfied (I died four times), return to the bonfire to refill your Estus Flasks, then put on your iron face.

Where to Stand
Get down the ladder and sprint to the opposite wall, behind the waterfall. When you get there, watch your Stamina refill and ready to block the first wave of Kalameet's fire. Now, see the chest? You are close. Refer to the image.




















Where to Aim
Two-hand your bow, look at the trees, and align your aim with the image (align with vertical of first tree, align with horizontal of second tree from right). I am unsure whether headshotting is possible.




















Shooting
Fire the second you see Kalameet. Early is better than late (you need the Stamina recharge to block twice). You should have enough time to watch your arrow fly and see a damage number show up (80 is very good damage, just don't go too far forwards). If a damage number does not show, then your arrow did not do damage, so check your footing and your aim.

Blocking
As soon as you see the damage, un-two-hand your bow, wait for your Stamina to get close to full, and hold block through two hits. Visual block timing is below, but it is much better to get a feel for the timing (so really do practise first). You will take a small amount of damage.










Adjusting
After blocking (the two hits should blow your shield back), lower your shield and take two steps forwards, and very slightly to the right (this compensates for the knockback of two hits from Kalameet's fire). If you go too far forwards, you will take three hits instead of two, and this will most likely kill you instantly, forcing you to do it all over again, and buy more arrows. From my own counting, Kalameet's flying attack cycle (for where you stand) occurs once every thirty seconds, giving you plenty of time to adjust. Chug an Estus if you need to, but be sure not to waste any. Play the long game.

Repeat the process, aiming, waiting, shooting, blocking, moving.


Eventually, Kalameet will be only a couple of hits from death. (At this point I scored a 345 damage hit. I don't know if it was a random headshot or a health mechanic for finishing the battle.) You should be experienced enough to know the greed is real, so be patient, and do what you've been doing for the past half an hour. Have your eleventh finger on the screenshot button, and watch for the final arrow.

Be sure to block. As the final arrow hits, Kalameet will fly down the canyon as normal. A few seconds later, you will receive the Calamity Ring, and a few tens of thousands of souls.

Don't expect any heroic music or a You Defeated Victory Achieved message.
Rather anti-climactic, I know.


The Aftermath
Go visit Haweye Gough for a short but unique dialogue.

Don't scroll down if you don't want to see the spoiler.





















Gough will still give you his Greatbow, just Talk to him some more.


All my screenshots have been taken in NG+++++, on a character with extremely high stats, so damage numbers may differ dramatically.