It is possible to fail BOTH quest lines if you kill or allow Anri to die. To make sure you are able to pursue one of their quests to completion you should never tell Anri where Horace is when she asks you (or you can kill Horace once you find him and after she starts asking) This will occur in the Catacombs of Carthus and Smouldering Lake zones.
If you kill him, Horace drops the Llewellyn Shield and the Shrinemaiden will sell his Executioner’s Armor.

UPDATE! It is possible to do both questlines in a single playthrough; credit goes to Buff Killer, and I'll let him describe the process:
"If you anger Yuria by hitting her three times, you can buy atonement from the statue of Velka under the undead settlement for a cost of your SL x 1000. So you can anger her before Abyss Watchers, kill Pale Shade for the claws, atone, and then before Pontiff anger her again, kill Pale Shade again for her set to spawn, and then atone again. Doing this won't break her questline. I did this and I have the claws, the pale shade set, the Duel Bow gesture, and I still married Ahri and have all the Dark Sigils, haven't completed the playthrough but there should be literally no reason I can't get the ending.
Note that atonement only works for angering her, doing things that outright break her questline like healing sigils, killing the assassin, killing Ahri, or killing her or Yoel, atonement obviously won't work."

- Anri's Path = Manikin Claws + Pale Shade set
Before you defeat Pontiff Sulyvahn, there is a chance to save Anri. When you meet Anri in the Church of Yorshka, hidden in the room are a group of statues. One of those statues is the Pilgrim of Londor. Attack and kill the Pilgrim here and now to stop the ceremony, if you fail to kill the Pilgrim here, Anri will end up dead.
Killing the Pilgrim allows you to use Anri as a White Phantom against Sulyvahn as usual. Later, when you go to face Aldrich in Anor Londo, Anri places a summoning sign outside the door. Use the sign and you can join Anri to fight their version of Aldrich. If you do so and successfully aid them in defeating Aldrich, Anri leaves Anri's Straight Sword with Ludleth for you.
Where Anri goes next depends on if you told Anri of Horace’s death. If you did, Anri travels to the grave site in Smouldering Lake. If not, Anri travels to the graves in the Cathedral of the Deep near the entrance. Either way, Anri finishes this long journey maddened, and attacks you on sight. Anri’s death completes this chain resulting in the Shrine Handmaid selling the Elite Knight armor set.

Additionally if you purposefully anger Yuria - the Pale Shade of Londor will invade you instead of being available as a summons, if you defeat him in Farron Keep and Irithyll Valley you will find his armor at Firelink Shrine. Thus it seems you ought to do this on your first playthrough combined with Anri's path, then complete Yuria's path on the 2nd playthrough. Just remember, for you to be invaded you need to have not killed the boss in the area yet (I believe) so I would reccomend getting 5x Dark Sigils spawning Yuria, then heal your Dark Sigil and/or kill Yuria before killing the Abyss Watcher to make the Shade invade you.
Killing Yuria has the added benefit of getting her Darkdrift katana and turning her ashes in to the Shrinemaiden will still give you access to all of Yuria's wares.

- Yuria's Path = Extra NPC summons, Morion Blade, Hollow's Ashes
Simply make sure to Draw Out your True Power with Yoel 5x before killing the Abyss Watcher, you can do this by jumping to your death repeatedly once you have at least one Dark Sigil. Once you do so, Yoel will die and Yuria will take his place. After this do NOT kill the Pilgrim to save Anri and continue the quest chain as normal to it's conclusion. Also, never "heal your dark sigil" with the Fire Keeper or this quest will fail, but using purge stones is fine. Both Yuria and the Pale Shade of Londor will be available summons to help you on the last boss if you follow their path to it's conclusion. If you summon Yuria and she lives through the fight, she will leave her armor and weapon at the Firelink Shrine. Interestingly Hollow's Ashes only appear in the Untended Graves if you never angered Yuria in your playthrough and are following her path.

Additionally, Yuria of Londor may ask you to eliminate Orbeck. Do so, and she rewards you with the Morion Blade. Or since he dies at the conclusion of his quest line, you can simply see his quest to completion and collect his ashes.

Both paths will give you access to the Chameleon spell, Anri's Straight Sword, Yuria's armor set and the Darkdrift katana. Both paths also have access to the Duel Bow gesture if you use the Pale Shade's summon sign next to the Farron Keep Perimeter Bonfire before angering Yuria; you do not need to kill a boss, simply summoning him is enough.

It has been confirmed to be possible to complete Sirris' Path then come back and do Leonhard's Path, thus if you want to do as much as possible during a playthrough save joining Rosaria's Fingers Covenant till after you complete Sirris' questline. However getting the Proper Bow gesture is mutually exclusive with Sirris' path. If you want the gesture by summoning Yellowfinger just before the 3-torch door leading to Abyss Watchers, you are going to have to sacrifice doing Sirris' path. And if you are going for the gesture you may as well kill Sirris after learning the Darkmoon Loyalty gesture from her, she'll drop her talisman and her set will unlock for sale.

- Sirris' Path
This Blade of the Darkmoon appears in Firelink Shrine after you reach Farron Keep. Speak to her, and then explore Farron Keep till you find the Dreamchaser’s Ashes. Deliver those to the Shrine Handmaid, and Sirris will appear again, offering the Darkmoon Loyalty gesture. At this point, her White Phantom sign appears in Farron Keep and the Cathedral of the Deep.
When you reach Irithyll Valley after you battle Sulyvahn’s Beast on the bridge at the entrance to the town, leave and return to check the front of the bridge. There you can find a summoning sign from Sirris. Enter her world and aid her against the invader Creighton the Wanderer. Successfully defend Sirris and she’ll show up in the shrine again to thank you, and give you a Blessed Mail Breaker. Creighton will now invade you in Irithyll Valley, and after defeating him you take his Dragonslayer’s Axe, Creighton’s Armor set also appears in the middle of the bridge at the entrance to the town.
Finally, she has one last summoning event directly in front of the Curse Rotted Greatwood’s room. To trigger it, you must defeat both the Greatwood and Aldrich in Anor Londo. Because slaying the Greatwood causes Hodrick to perish, you may wish to visit him before killing the Greatwood.
Successfully aid her in her battle when she summons you to acquire the Sunset Armor set, and she returns to the Shrine and asks to swear an oath of knighthood to you. In addition, she leaves the Sunset Shield by the grave of her grandfather. To find it, look off the right side of the cliff, just past the doors from Iudex Gundyr’s room. Accept her vow and she appears as a White Phantom for Dragonslayer Armour and the Twin Princes battles in Lothric Castle and the Grand Archives. Complete those battles, and you later find her corpse by her grandfather’s grave, along with the Sunless Talisman.

Additionally, as hinted at above, the only way to meet Hodrick alive is to locate a Hollow Manservant wearing a cage on its back in the Undead Settlement. Approach it quietly from behind and you can press the use key on the cage to enter the Pit of Hollows - do this before killing the Curse Rotted Greatwood or he will die

- Leonhard's Path
Leonhard first appears in Firelink Shrine after you light the Tower on the Wall bonfire in the High Wall, or after defeating Vordt. Speak with him for 5 Cracked Red-Eye Orbs
Once you light the Cliff Underside bonfire in the Undead Settlement, or defeat the Curse Rotted Greatwood and you have a Pale Tongue in your inventory, Leonhard reappears in the shrine. Speak with him to acquire the Lift-Chamber Key. You can use this key to descend through a locked door in the High Wall of Lothric, beneath the Tower on the Wall bonfire. Deep in the chamber is a Darkwraith. Defeat it, and you will acquire a full Red Eye Orb, which can be used for unlimited invasions of other players.
Your next encounter with Leonhard only occurs if you join Rosaria’s Fingers in the Cathedral of the Deep and offer or use at least one Pale Tongue (though be aware that doing so antagonizes Sirris of the Sunless Realm if you are pursuing her questline). Leonhard appears at the exit to her chamber after you do so.
Still later, after you have joined Rosaria’s Fingers and you have reached the Profaned Capital bonfire or defeated Yhorm the Giant, Leonhard slays Rosaria. Return to her body to find the Black Eye Orb. Take the Orb to the highest room in Anor Londo, it will activate, allowing you to invade Leonhard and slay him to recover Rosaria’s Soul, as well as the Crescent Moon Sword and the Silver Mask. This also causes the Shrine Handmaid to sell Leonhard’s Armor set. Return her soul and she revives as though nothing happened, it may be a bug but atm you can keep her soul for yourself and still use her services while she is dead.

1) Check the dead giant tree just outside the Firelink shrine each time after being invaded for a chance of a seed spawn
IMPORTANT NOTE! Unlike in DS2, the tree's appearance does NOT change to indicate "a seed has fallen," you have to activate the "examine" each time to see if one is available or not

2) If you pick up all of the white tree branches and return, you find the giant of the Undead Settlement has peacefully expired, leaving the Hawk Ring... or you could just kill him for it plus some souls.

3) Allowing Greirat to pillage the Undead Settlement is safe, but if you let him Pillage Irithyll without either Siegward present, or telling Patches where he went; he will die in Irithyll, leaving his Ashes in the sewer. And if you send him to pillage Lothric Castle, he dies regardless.
UPDATE: I am told for Patches to save Greirat, he needs to still have all of the Onion knight armor on him. Additionally, I am told it is possible for Greirat to survive the 3rd pillaging if you completely clear out Lothric Castle before sending him, but the exact condition for him surviving the trip is unknown.

4) If you give Irina of Carim the Deep or Londor Tomes and then purchase any Dark Miracles from her, she falls to darkness and Eygon will kidnap her to try to save her from your corruption.
However, if you purchase all of the holy Miracles, she becomes a Fire Keeper, and moves to the basement of the tower just outside the Firelink Shrine.
A much better character to learn dark magic from is Karla the Witch, so give her the Deep and Londor Tomes instead of Irina.
Additionally, if you do not anger Eygon, his last appearance is as a White Phantom for the Dragonslayer Armour battle, after which his corpse appears in Irina’s original cell in the Undead Settlement.

5) Orbeck’s pact with you is a promise to deliver him scrolls for study. Fail to do so by killing four bosses without giving him a single scroll and he departs forever.
To acquire his Slumbering Dragon Ring - purchase Aural Decoy, Farron Flashsword, and Pestilent Mercury.
Finally, if you manage to provide him with all of the scrolls in the game and buy all of his spells, he leaves the shrine. You can then find his White Phantom summon sign on the battlements near the Twin Princes battle in the Grand Archives. After defeating the Twin Princes, you will find him dead in the Grand Archives where you can pick up his ashes.

6) Speak with Hawkwood after defeating the Greatwood or Crystal Sage bosses to acquire a Heavy Gem. Then defeat the Abyss Watchers and speak with him again to acquire the Farron Ring. After you have exhausted Hawkwood’s dialogue and defeated all three of the bosses, Hawkwood departs, leaving Hawkwood’s Shield at the grave. At this point, you won’t see Hawkwood for a long time. He’ll appear again as a White Phantom sign in the Consumed King’s Garden.
After that, if you find your way to Archdragon Peak, his White Phantom sign can be found not far from the third bonfire. Activating it causes Hawkwood to travel up to the shrine at the end of the trail, where he prays and vanishes. If you follow suit and use the Path of the Dragon gesture at the shrine and acquire the Twinkling Dragon Torso Stone, Hawkwood leaves a message with Blacksmith Andre in the shrine, challenging you to a duel. If you travel to the Abyss Watcher’s room in Farron Keep and face Hawkwood, defeating him earns you the Twinkling Dragon Head Stone, but losing costs you the Torso stone.

7) If you summon the white phantom Great Swamp Cuculus in Smouldering Lake and defeat the Old Demon King, you can then journey to Cornyx’s original imprisonment site in the Undead Settlement where you will find the Spotted Whip and a set of Cornyx’s garb.

8) There is a massive tower near Anor Londo that you can’t seem to reach. Start at the Anor Londo Bonfire and backtrack to the highest tower in Irithyll. Use the mechanism of that tower to lower the walkway. From the tower’s lower setting, there is an invisible bridge. Walk from there over to the nearby tower, but a bit lower than where you’re standing. Hop off to get onto the balcony of that tower and use the Bonfire there. This leads to Yorshka, a Covenant leader.

9) Try killing Ludleth, you'll receive the Skull Ring. Ludleth will return from the dead, and he doesn't seem to mind.

10) Havel's armor appears on Farron Keep bridge behind the Stray Demon after you defeat him in Archdragon Peak.

11) Do NOT forgive Patches and he will give you a Rusted Gold Coin, also I was told that if you kill him he drops the Catarina set for free - this is best done after getting both rusted coins and only on your first playthrough since on subsequent playthroughs you should already have a set of Catarina armor from finishing the Onion Kinight's questline
IMPORTANT NOTE! It seems Patches must have the Catarina set for sale for him to drop it, if he does not have it for sale yet, do not kill him

12) The giants in Cathedral of the Deep and Profaned Capital drop 1xLarge Titanite Shard + 4x Dung Pies each, these are guaranteed drops but they will disappear if you you do not grab them before dying or reloading

13) Kill NPCs before progressing to NG+ - Yorshka drops a unique chime, Karla drops her set so you wouldn't have to spend souls on it, Yuria drops the Darkdrift Katana, Patches drops the Horsehoof Ring and a Winged Spear, the Shrinemaiden in Untended Graves drops the Priestess Ring, and Irina drops a free Tower Key

http://darksouls3.wiki.fextralife.com/Illusory+Walls
http://darksouls3.wiki.fextralife.com/Invading+NPC+Phantoms

For more details you can also refer to my Completion Checklist:
http://steamproxy-script.pipiskins.com/sharedfiles/filedetails/?id=668170573

http://steamproxy-script.pipiskins.com/sharedfiles/filedetails/?id=665026050
http://steamproxy-script.pipiskins.com/sharedfiles/filedetails/?id=672914215
http://steamproxy-script.pipiskins.com/sharedfiles/filedetails/?id=684708376