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The one major player snatched from Dark Souls who was dropped whole cloth into Elden Ring, Patches the Untethered is the same as he ever was: Shifty, greedy, cowardly, and a poor liar. Listening to his advice is sure to get you into trouble - but doing so can also yield great rewards.
This guide will cover the entirety of Patches' questline in Elden Ring. Be warned, though - Patches will send you into some dangerous territory, and getting back out again with your skin intact is not guaranteed.
Step One - Meet Patches
Your first meeting with Patches takes place in Murkwater Cave, in Limgrave. Walk down to Lake Agheel and follow the river that leads upstream. Pretty soon you'll find Murkwater Cave on your left. As you approach you'll be invaded by Bloody Finger Nerijus, a dangerous opponent, though Bloody Finger Hunter Yura will appear shortly thereafter to help you. Hold off Nerijus until Yura shows up to save the day. Running is a viable tactic if Nerijus is too much to handle on your own.
Step into the cave. It's a short trip to the boss fog, with a few minor bandits inside to stymie your progress. Once you breach the boss fog you'll wind up in a small cavern, by a campfire, and Patches will appear and attack you once you try to open his treasure chest. Patches tends to hide behind his shield and try to poke you to death, so circle around him and attack after he's made his own attempt.
Once you do enough damage Patches will plead for mercy and stop attacking. End your assault and the battle will similarly end a few moments later. This will earn you a Golden Rune  and the Grovel for Mercy Gesture. Patches will thereafter open a shop.
After you've met Patches you'll have the option to summon him for the battle against Starscourge Radahn. If you do, however, he will show up and promptly leave again. Very helpful.
Step Two - Teleporter Shenanigans
If you speak to Patches you can ask him about the remaining treasure chest in his cavern. He'll be vague about it, hinting that the right person needs to come along and open it. Do so yourself...
... and you'll be caught in a teleporter trap. Once Patches is done gloating and chastising you you'll be whisked off to the Mistwood and deposited a short way from the Minor Erdtree, near several Giant Bears. If you're visiting Patches early in the game you definitely don't want to fight these things, so either sneak away or hop on your horse and gallop out of there before one kills you.
Return to Murkwater Cave. Patches is flabbergasted that you escaped, but will otherwise provide you with the usual range of merchanting services.
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Step Three - Move to Liurnia of the Lakes
If you leave Murkwater Cave and come back Patches will likely be gone. This marks his move to Liurnia of the Lakes, to the north of Limgrave. Patches has set up camp at the Scenic Isle Site of Grace. If you've activated the Academy Gate Town Site of Grace you can find Scenic Isle by riding almost directly south through the swamp. The Guidance of Grace should also lead you there from the southern entry point of Liurnia of the Lakes.
Patches has some new wares, and you have two conversational options. The first option has you speaking to Rya, a talent scout of sorts for Volcano Manor; the second has Patches suggesting you try out something very dangerous. Both options will ultimately lead you to Volcano Manor, a Legacy Dungeon on Mt. Gelmir. Since it is more directly related to Patches, we will explore the second option.
Step Four - The Iron Virgin
When prompted Patches will tell you about Iron Virgins, big, metal creatures that try to ensnare you inside themselves. Typically when fighting one you don't want this to happen, but Patches suggests that allowing a particular Iron Virgin at the Academy of Raya Lucaria to grab you will actually teleport you to the Erdtree. Sounds pretty far-fetched, but let's try it out.
Head to the Academy and make your way through until you find an enormous lift, located after the graveyard full of zombies but before the Schoolhouse Classroom Site of Grace. If you hop onto the lift at its highest point, up a hill from the aforementioned Site of Grace, you can ride it down into a pit. The Iron Virgin is here. Allow it to grab you and kill you. Make sure the grab attack is what kills you, not the Iron Virgin's other attacks.
When you return to consciousness you'll be at Volcano Manor, not the Erdtree, and you'll be unable to teleport away. The nearest ledge to the main part of the Manor is just out of reach of your jumps, so you'll need to use a rear exit filled with Giant Bats, Fire Slugs, and a few Albinaurics to escape. At the end of the path is the Subterranean Inquisition Chamber Site of Grace, and if you're not prepared for this area you can teleport away once you've activated the Site of Grace.
If you feel prepared, on the other hand, jump off the ledge near the Site of Grace and you'll find a path across the lava and into a cave. This leads to a boss fight with a pair of Abductor Virgins, one with spiked wheels for arms, the other with giant blades. This is a tough fight if you don't call in help to keep one of the Abductor Virgins busy, though you can manage by staying on the edges of the room and only going after the Abductor that's currently trying to rush you. You'll earn an Inquisitor's Girandole for defeating the Abductor Virgins.
This will also reveal the Abductor Virgin Site of Grace, and ahead of that is a steep jump down to the Altus Plateau. So if you haven't been to this area yet, congratulations.
Step Five - Volcano Manor
Patches' next appearance is at Volcano Manor. Once you've reached the manor and completed one of Tanith's assassinations the NPCs in the manor will be changed around a bit, and Patches will appear in the entry hall. Speak to him and he'll reveal more of his intentions, as well as open up shop again.
Refresh the area and speak to Patches again. He'll give you the Letter to Patches, which contains an assassination target: Great Horned Tragoth. Tragoth's invasion sign is located at the Ruin-Strewn Precipice, near the Magma Wyrm Site of Grace. Tragoth is a summonable NPC in a number of fights throughout Elden Ring - including the Magma Wyrm Makar fight, within whose battle arena you can assassinate Tragoth - and killing him will remove the possibility of summoning him in the future. Tragoth is a powerful opponent if you do fight him, with a crossbow for ranged attack and a heavy hammer for slow, close-quarters fighting. Wait until he swings his hammer before you hit him yourself.
You'll earn the Bull-Goat Set for defeating Tragoth. Return to Volcano Manor and speak to Patches about your success. He will, quite clearly, take credit for your work. Reload the area and speak to him again to ask about a reward. He'll hand over the Magma Whip Candlestick.
Speak to Patches again after completing Volcano Manor by defeating Rykard, Lord of Blasphemy. He doesn't seem too upset, and says he's heading off somewhere else. When you come back next time he'll be gone.
Step Six - Shaded Castle
Your final meeting with Patches is in the Shaded Castle. You'll find him on the shaded bridge covered in statues, just before you reach the Elemer of the Briar boss fight. He'll give you Dancer's Castanets and slump over. If you stab him - and you probably should, since you'll never see him again - Patches will immediately disappear, dropping Patches' Bell Bearing, a Spear +7, and the Leather Set.