The Fume Knight is a tough customer who uses a mixture of rapier and ultra greatsword attacks, so you will need to be on top of your game to deal with him. His attacks will eat through your shields quickly if you're not careful. Good thing you've got this guide.
Move to the sword near the middle of the area to start this fight. In the initial phase, the Fume Knight uses a rapier-style weapon and an ultra greatsword. Stay close to him and strafe a lot to avoid a bunch of attacks from the latter. Obviously keep a close eye on your stamina and let it recharge as sensibly as possible - the greatsword attacks eat through it quickly. The Fume Knight usually strikes twice with the rapier and then once or twice with the greatsword, but he takes a while to wind up for the latter, so you should be able to read him.
Sometimes he just swings the greatsword. This variation comes from the opposite side and may hit you even if you're strafing right, eating up a lot of stamina when you block. He will do this two or three times in a row without hesitation, so rolling is a good idea if you can.
If you move away from the Fume Knight, he will go with a lunging rapier attack or else a massive swing of the greatsword. Either will reach a long way, so don't think you're safe just because you've created some space. And if the Ashen Idols were left untouched before, don't let him come that way or he'll heal up, which is infuriating let me tell you.
Not content with all this, the Fume Knight will power up after a little while. This makes the rapier disappear and instead the ultra greatsword becomes engulfed in magic, buffing all his subsequent attacks between now and the end of the fight in additional magic damage.
Stay close and strafe round him to the right. If you were blocking before, you want to be dodging now. Don't fret if this isn't your forte, though - you should get used to his lengthy animations and be able to time your evasion.
Should the Fume Knight plunge his sword into the ground, there are a couple of possible responses. The next attack is a 360-degree spell that sends fireballs every which way along the ground. Staying close means you need to roll with very precise timing to avoid them. Getting back out of the way gives you more room, but don't get complacent because if you take a hit from one you'll receive tremendous damage.
While the fireball attacks continue, strafe around and attack as and when makes sense. The Fume Knight will take some serious hits if you've levelled up smartly and packed strong weaponry and shouldn't last forever. This fight is all about avoiding the magic ultra greatsword attacks and if you can manage that, you'll be done in short order.
Once he's down, that's it! You'll get a Soul of the Fume Knight for your trouble and you've beaten the Crown of the Old King DLC. But of course, there's plenty of other loot to be found if you want to venture into the Iron Passage side area.
That's it for the main boss, but there's more. Don't miss all the Crown of the Old Iron King weapons, rings and other loot.