This is a very hard two phase fight; the transition from the slower-paced first phase to the often chaotic second phase can be a little jarring, and will likely lead to a few deaths. You may be great at Souls (I consider myself above average), but this fight can shove your face in the sand and laugh at you if you aren't prepared. Once you accept that, then you can ruin this hollowed King's day. To access this fight within Archdragon Peak, you first need to acquire the "path of the dragon" gesture after the Oseiros boss fight in the Consumed King's Garden. After that, return to Irithyll Dungeon and use the gesture next to the bodies where you acquired the dragon torso stone, then you will be teleported to Archdragon Peak. Continue through Archdragon Peak until you reach a gigantic bell (you can't miss it), pull the nearby lever and the boss will become accessible.
My personal ring setup was the ring of favor, thunder stoneplate ring (for the second phase of the fight), cloranthy ring (extremely helpful if you are dodging often in the second phase, and the silver serpent ring (this can be swapped out for a fire stoneplate to make the first phase easier).
King of the StormFor the first phase of the fight, you will be fighting the King of the Storm (a very recognizable figure in the Souls mythology for anyone who has played DS1) on top of his Thunderdrake. I would suggest using a weapon with an upward/downward strike in order to capitalize on more opportunities when the dragon is vulnerable, otherwise you will only be able to hit his head (which takes far more damage than the legs) when it is on the ground.
Fire BreathThe dragon will cock his head and release a concentrated stream of fire. Once you learn the tell, this is an extremely easy way to rack up damage on the head/neck for the first phase.
Aerial FirestormThis attack will look very familiar to anyone who has fought Kalameet in DS1, but it can be a little more difficult to dodge. As soon as you see the dragon fly straight up, unlock and run/roll as fast as you can in the opposite direction. If you are having difficulty dodging this, then the fire stoneplate ring will be your best friend for the fight.
Sword SwipesThe King will swipe/thrust from multiple angles in a series of up to 3 attacks. The swipes are deceptively slow, and you will likely learn the timing just from dodging too early a few times. Simply rolling into the swipes or far enough away from the spear lunges will leave the dragon open to a counterattack.
Lighting Spear with Spear Follow-upThe dragon will circle you in the air and the King will throw a lightning spear. Lock on and dodge as soon as the King jerks his hand to throw the spear. The King will follow up the lightning spear with a swipe of his spear every time. The timing for this is pretty forgiving and predictable after seeing it a few times.
The Nameless KingI don't think anyone would argue against this being the most difficult fight in DS3, and one of the harder fights in the Souls series. The King has a very diverse moveset with a series of deceptively slow attacks, some very fast attacks, and lightning attacks. Describing the individual timing of each of his attacks would be of little use, but my video below includes his entire moveset. It is worth mentioning that you can occasionally stagger him and follow-up with a high damage attack if you press rb next to him (very similar to the visceral attack from Bloodborne).