Siegward of Catarina is the Dark Souls 3 incarnation of the Onion Knight, also known affectionately as Onion Bro, who first appeared in Dark Souls as Siegmeyer of Catarina. The name references the armour, which strongly resembles an onion (and it's fun to consider an armourer making the full set). You can run into Siegward several times in the game, and if you do it right he'll help you in the boss fight against the Yhorm the Giant, a Lord of Cinder.
The first time you run into Siegward is at the Undead Settlement, at the tower with the giant at the top (you know, the giant hurling giant spears every which way but loose). You can get there by starting at the Cliff Underside bonfire, going out onto the roofs and crossing the bridge over the chasm on your right. As you run into the tower Siegward will come up in the lift and grumble about not knowing how to get up to the top of the tower when you speak to him. After you figure out the trick lift (by getting on, immediately getting off, and waiting for the second platform to come down) you will, on the way back down on the lift, hear Siegward's trademark "Hmmm…" about half way down. If you look to the side of the tower about where you hear this you'll see a platform that you can jump onto from the lift, though it takes some good timing, because falling from that height will kill you.
From jumping onto this platform you can find Siegward sitting on a wall looking at a fire demon in a village square below you. What you need to do is run down there like an idiot and initiate combat with the demon. Siegward will hop off the wall to come and help you, because he's a billboard sort of bloke. Once you kill the demon together he'll toast you, and instantly fall asleep. You have to fight the demon with him for Siegward to turn up later in the game. Just chatting to him at the lift isn't enough.
Once you've opened the main doors at the Cathedral of the Deep you can go back to the Cleansing Chapel bonfire and look into the well beside the front doors of the chapel. You should get a dialogue prompt and, low and behold, Siegward has got himself stuck in the well without any armour on.
Go back to Firelink Shrine and go up into the tower behind the shrine (if you haven't already you'll need to buy the key to open it from the Shrine Handmaid). As you get on the lift to the very top you'll hear a door clanging. Go back to the bottom and you'll see you've been locked in by a man called Unbreakable Patches (and Unbreakable Patches is a dick). Once you get out, either by dropping from the bridge carefully, via the tombs sticking out of the wall, or just by dying, you can find Patches on the top level of the shrine. He'll ask for forgiveness, and you should give it to him. He'll then become a vendor, and you can buy Siegward's armour from him. You can also kill him to loot the armour back, too, which is a much cheaper option.
Go back to the well at the Cathedral of the Deep and speak to Siegward to return his armour. Job done.
It's worth noting that, if you sent Greirat to loot things at Irithyll and Patches is still alive at this point, Patches will start pestering you for Greirat's whereabouts. If you tell him he will straight up murder Greirat. Because Patches, as noted earlier, is a dick.
From the Distant Manor bonfire run out onto the lake and the right, into the small basement sewer area full of those long–haired insect spider things, and up into the kitchen of the house. Siegward will be sat by the fire at the end, and will have a little chat and another toast with you. You need to find him here before you go to the Irithyll Dungeon, or it'll disrupt the questline with him and he won't appear to help you fight Yhorm.
The next time you meet Siegward he'll be locked in a cell, which is technically at the bottom of the Irithyll Dungeon, but you can only get to the door via the Profaned Capital. To get Siegward out you need to have first found the Old Cell Key in the Irithyll Dungeon, and then need to start at the Profaned Capital bonfire to find Siegward's cell.
When you go to fight Yhorm the Giant a cutscene will play where Siegward arrives in the arena and calls Yhorm out. He'll then help you in the fight, which is substantially easier if you have him along. If you speak to him after the fight he'll reference Yhorm being his old friend. It's a bit of a sad story, really. If you leave and return to the boss arena later he's left all his gear there for you. Good old Onion Bro.
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