Nepheli Loux is an Elden Ring NPC you'll first encounter as you make your way through Stormveil Castle. She's a dedicated, serious warrior who offers to help you fight Godrick the Grafted. Whether you accept her help or not, you'll embark on her questline. Here's how to complete it.
UPDATE 3/17/22 11:54 a.m. ET: Elden Ring Patch 1.03 went live last night, and it made the rest of Nepheli's quest line available to complete. The full walkthrough is available here.
Nepheli Loux Starting Location
The first time you meet Nepheli Loux will be in a small room in the courtyard outside Godrick the Grafted's arena. The nearest Site of Grace is the Secluded Cell. From there, head south into the courtyard past the two soldiers and the giant. At the far end of the courtyard, you'll find a room with Nepheli standing inside. Exhaust her dialogue options, then go fight Godrick. (Good luck!)
Nepheli Loux Second Location
After defeating Godrick and exhausting the dialogue options with Gideon Ofnir, return to Roundtable Hold and you'll find Nepheli standing outside Gideon's study. You'll learn she's his adopted daughter by exhausting their dialogue. You'll also receive the valuable Arsenal Charm.
Nepheli Loux Third Location
The next place you find Nepheli will be in the Village of the Albinaurics. You should see her along the main path through the area, but if you miss her make your way back to the path leading up to the Village of the Albinuarics Site of Grace from the south. She's standing under the bridge that leads to the Omenkiller boss. Talk through her dialogue options, then go kill the Omenkiller.
Nepheli Loux Fourth Location
Nepheli's next in-game location can be found by returning to the Roundtable Hold and heading down the stairs next to Master Hewg, the blacksmith, and turning left.
At this point, Nepheli's quest line begins to intersect with that of Preceptor Seluvis. If you've met him at Ranni's Rise in the Three Sisters sub-region, you can then find him at Seluvis's Rise nearby. When you do, he'll give you Seluvis's Potion and tell you to have Nepheli drink it.
If you do as he says, you'll find he's turned her into a puppet and stashed her in his secret room; you'll be able to obtain her Ashes. Alternatively, you can talk to Gideon Ofnir about Seluvis's plan, and he'll offer to dispose of the potion in secret, leaving Seluvis in the dark — or you can feed it to the Dung Eater provided you've progressed his quest line enough that he is bound to a chair and accepting Seedbed Curse. In that case you'll receive his Ashes instead of Nepheli's.
Regardless of which option you choose, you'll now be able to learn sorceries from Preceptor Seluvis.
If you opted not to give Nepheli the potion, you'll have the chance to give her the Stormhawk King you find in the Chapel of Anticipation. To reach the Chapel (which you may recognize from the start of the game), you'll need to head to the Four Belfries in the northeast of Liurnia of the Lakes. These four Belfries on a hill can send you to several locations via waygate, one of which is the Chapel of Anticipation. You'll need an Imbued Sword Key, but don't worry if you don't have one: the belfry highest on the hill will give you one for free.
With Imbued Sword Key in hand, look for the waygate labeled Precipice of Anticipation in a nearby message. Use the key on the imps, then head through to find yourself back at the Church of Anticipation. Proceed through the area, defeating the Grafted Scion that killed you at the start of the game, and return to the chapel itself.
Facing the chapel, head to the right and you'll find a previously unlocked door now open. Climb the stairs and loot the item there to pick up the Stormhawk King. (There's also a chest inside the chapel's second floor to loot.)
Return to Nepheli and hand her the Stormhawk King. Exhaust her dialogue options.
Nepheli Loux Fifth and Final Location
To finish this quest, you'll need to have completed Kenneth Haight's quest to the point at which he says he's going on a quest to find a new lord of Limgrave. You must also have defeated the Shardbearer Morgott, the Omen King, and Maliketh the Black Blade must still be alive.
If you meet these criteria, return to the throne room beyond the Godrick the Grafted arena. There, you'll find Nepheli and Kenneth, and Nepheli will tell you she's taken up leadership of Limgrave. She'll reward the player with an Ancient Dragon Smithing Stone. If he's still alive at this point, Gatekeeper Gostoc will also be in the throne room, and will sell a second Ancient Dragon Smithing Stone for 20,000 Runes.
The original final paragraph of this guide appears below:
Thanks to data mining, we know that Nepheli Loux's quest line was meant to continue beyond this point. Players would have been able to restore her to the throne in Stormveil, making her Lady of Limgrave and fulfilling Kenneth Haight's quest for a new ruler of Limgrave. Voiced dialogue for this possibility has been uncovered in-game using memory editing. Unfortunately, there doesn't appear to be a way to access this content through standard play.