This ending requires some specific interaction with a few NPCs. These are the steps that I followed. Be sure to exhaust all dialogue whenever talking with an NPC.
1) Talk to Yoel of Londor when you first reach the Undead Settlement and say "yes" so he will relocate to Firelink Shrine.
2) "Draw out your true power" (level up) five times with Yoel. The first level up is available as soon as he gets to Firelink Shrine. After that, you must die twice before he offers to give you another free level. I suggest suiciding off the nearest cliff and getting your five free levels immediately. Leveling up with Yoel gives you Dark Sigils, which cause you to turn hollow when you die (causing a change in physical appearance- nothing else). The Firekeeper can cure the Dark Sigil if you return a Firekeeper Soul to her, but this breaks the questline and voids this achievement, so don't do it. After leveling up five times through Yoel, he will die and Yuria of Londor will appear.
NOTE: Yoel will die when you enter the Catacombs of Carthus after killing the Abyss Watchers so be sure to get your five levels before that.
3) Talk to Yuria in Firelink Shrine.
4) Talk to Anri and Horus at the Halfway Keep bonfire in the Road of Sacrifices.
5) Defeat the Deacons of the Deep in the Cathedral of the Deep (I summoned Anri and Horace, not sure if it matters).
6) Talk to Anri and Horus in Firelink Shrine.
7) Talk to Anri in the Catacombs of Carthus. From the Abyss Watchers bonfire, enter the catacombs, head across a long bridge and enter the next room, turn right and drop down to a lower level, then head to the back/left area and go through a passage and you'll find her.
8) Talk to Anri at his/her next location in the Catacombs of Carthus. From the Catacombs of Carthus bonfire, head left and then through a hallway just off to the right (you had to lower a gate from the other side to be able to get through) and you'll see a large wooden bridge. Take a path on the right just before the bridge and you'll see Anri at the end.
9) Drop down from where Anri is to a platform that leads to the far side of the bridge. Attack the supports so the bridge collapses, then use the broken bridge as a ladder and climb down. Work your way to the Smouldering Lake area below. Follow along the right side wall in the open lake area where you get pelted with large projectiles and you'll enter a cave with a room at the end where you'll find Horace, who is aggressive to you. Kill him.
10) Talk to Anri again next to the bridge. Choose "Tell about the Smouldering Lake."
11) Talk to Anri at the Church of Yorshka bonfire in Ithiryll of the Boreal Valley.
NOTE: There are some human statues in the corner of this area and one of them is a pilgrim enemy in disguise. If you attack the statues, you can kill it (and receive the Chameleon sorcery). DO NOT DO THIS or it will end the questline and void the achievement. This pilgrim kidnaps Anri to advance the questline.
12) Defeat Pontiff Sulyvhan in Ithiryll of the Boreal Valley.
13) Return to Firelink shrine and talk to Yuria. She will tell you that your spouse is ready.
14) Go to the Darkmoon Tomb (located behind a illusory wall in a room right before you reach the twisting/rising platform that you use to reach Anor Londo) and talk to the pilgrim there. You'll receive a quest-related item.
15) Interact with Anri on the altar.
16) Talk to Yuria in Firelink Shrine.
17) Proceed through the rest of the game. Upon defeating the final boss, simply interact with the bonfire to trigger this ending.
Remember that if you return the Firekeeper Soul from the top of the locked tower in Firelink shrine to the Firekeeper, she will offer to cure the Dark Sigil. DO NOT DO HAVE HER DO THIS or Yuria will become angry and leave and you won't be able to get the achievement. After completing the game and getting the achievement, feel free to have the Firekeeper cure you (which will happen automatically when you start the next playthrough).