Pontiff Sulyvahn is a bit of a bastard, if we're honest, who, like almost everyone in this game, is non-specifically angry at you and wants you out of his church right this second thank you very much. He also appears to be keeping a woman prisoner in a tower elsewhere in the city, but this isn't explained with any depth, because obviously it isn't. Sulyvahn is a hard boss, but you can take him down if you're ready for what he throws at you.
Once you've opened up the shortcuts around the main area of Irithyll you can run from the Church of Yorshka bonfire and just keep going left to get to the boss fog for Pontiff Sulyvahn. The good Pontiff does a lot of magic and fire damage, and this on top of hitting you with a big sword, so it's advisable to stack any items you have that can increase your defense to them. When you enter the boss arena he approaches very slowly, so you have plenty of time to gear up your consumables. He does have a fair turn of speed in the actual fight, however, so you might want to consider a faster weapon like a sword, or using spells with quicker cast times on them, to get more hits in with every opening he gives you.
Pontiff Sulyvahn's attacks are similar to the Abyss Watchers. He has one long weapon and one shorter one, and his greatsword is also on fire. His attacks are fast, he chains them together in spins, and they have a wide arc of damage.
There are a few tactics open for melee players. If you're at a distance from him you can draw him into a big slash forwards which is relatively easy to dodge either side of as it lands, to get in a couple of hits or a backstab. This will most likely be his first manoeuvre when you enter the boss arena and he starts walking at you, all slow and statesman like. Keep doing this – backing off, drawing him out, getting some hits in – until you've chipped him down.
If you're a tanking shield user you can lock on to him and strafe around. When you stay close to him Sulyvahn likes to chain a bunch of sweeping attacks together, but turtling under your shield (if you've got a good enough shield and enough poise) you can absorb most of the damage, until he does a heavy swing or thrust that he needs a pause to recover from, which you can use to hit him. If you're good at parrying then Sulyvahn is, weirdly, easy to parries, so you can use that to wear him down quickly. The other option when staying close by him is to dodge the attacks by fast rolling around and then popping up to smack him, but this needs high stamina levels or you'll be all out of it when you go to actually hit him. If you're using this tactic it's really useful to have an item like the Carthus Milkring (found in the Catacombs of Carthus) which will obscure your rolling.
This is, once again, a harder fight for spellcasters. You need to keep as much range as possible and avoid spells with a long cast time so you can dodge when you need to. Sulyvahn can cover a bunch of ground when he feels like it so watch out. If you're a pyromancer, however, and you've stacked the relevant stats high enough, and reinforced your pyromancy flame, you can do a lot of damage to Sulyvahn very quickly.
When he gets down to half health Sulyvahn will drop to his knees, which is a cunning trap because if you run in to get easy hits you'll take area of effect damage from the spell he's casting (which appears to be 'Spell to Grow Small Wings That Look A Bit Like Tree Branches'). He'll then stand up and slowly generate a purple ghost of himself which will, surprise surprise, follow the same moveset and do the same damage as the main Sulyvahn. The ghost will often perform an attack a couple of seconds before Sulyvahn himself does, so in that sense it's quite useful.
This phase also adds some new attacks. Sulyvahn can use his little twiggy wings to leap high in the air and smash back down, and has some magical projectiles (one a straight dart, the other a horizontal arc that's a little harder to avoid).
Aside from the new attacks, and avoiding the clone, the second phase is business as usual. You can get a few cheap shots in on Sulyvahn while he produces the clone because he stands mercifully still whilst it steps away from him. If you've got a beefy enough attack on you, you can take out the clone at the same time, before it has a chance to get going. It's also incredibly weak to fire damage, so a Pyromancer can take the ghost out super fast, and if you're not one of those you can use firebombs instead. It might take a few goes, but you'll get Sulyvahn in the end.
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