Brand of Vanity

Jeanne d'Arc (Stage 1~5)

Barong (Stage 6~9)

Quetzalcoatl (Stage 10)

Wave 1

Sphinx	Power	Mermaid

Resistances
Sphinx	-	Nu	Wk	-	-	Rp	Wk
Power	-	-	-	Rs	Wk	Nu	Wk
Mermaid	-	-	Rs	Wk	Rs	-	-
Battle Speed			12,200

Wave 2

Sarasvati	Sphinx	Power

Resistances
Sarasvati	-	Wk	Nu	-	-	-	Wk
Sphinx	-	Nu	Wk	-	-	Rp	Wk
Power	-	-	-	Rs	Wk	Nu	Wk
Battle Speed			13,200

Wave 3

Sarasvati	Quetzalcoatl	Sphinx

Resistances
Sarasvati	-	Wk	Nu	-	-	-	Wk
Quetzalcoatl	Rs	Rs	-	-	Rs	Rs	Wk
Sphinx	-	Nu	Wk	-	-	Rp	Wk
Battle Speed			16,533

Auto Party

Explanation

The demons here are all weak to Dark, hence the usage of demons that are Dark magic users. Enemies here tend to heal, and due to Sphinx's Tetra Shift, phys attackers aren't very reliable.
Garuda makes this a lot easier due to having Repel Fire and Null Force, both elements that Quetzalcoatl uses. If you don't have it, bringing at least one Null Fire demon (preferably one that can Dark DPS, like Red Tsukuyomi) and one Null Force demon is very useful.
Pazuzu is a lot tankier of an option than Feng Huang, and boasts multiple nulls to prevent Sphinx's Mahamaon / Quetzalcoatl's Mazandyne.
Other two slots are for Dark DPS.

Example Party

Fire Null + Dark DPS	Healer	Dark DPS	Dark DPS
Tsukuyomi	Pazuzu	Beelzebub	Anubis
Mamudo	Resist Ice	Mudo	Mudo
Resist Phys	Diarama	Dark Boost	Mamudo

Dark DPS options include: Alice, Anubis, Beelzebub, Rangda, Black Frost, Kaiwan, Red Tsukuyomi

Healer alternative is Feng Huang or Asherah.

Teal Jikokuten is also a possibility if you have lots of Fire/Wind Drain demons, to force Quetzalcoatl to lose more turns due to Suppress Stance: Drain, but remember that it's a physical attacker.

Divine + at least 1 Ward set for Sarasvati to use Silent Prayer. Red Tsukuyomi can use Life or Spell instead of Divine because Lunar Blessing causes its awakened Mudoon to only cost 3 MP.

Videos of clear:

Additional discussion:

Quetzalcoatl (Stage 11)

Wave 1

Makami	Matador	Mermaid

Resistances
Makami	-	-	-	-	-	Rs	Wk
Matador	Rs	-	Wk	-	-	Rs	Rs
Mermaid	-	-	Rs	Wk	Rs	-	-
Battle Speed			21,433

Wave 2

Makami	Sphinx	Mermaid

Resistances
Makami	-	-	-	-	-	Rs	Wk
Sphinx	-	Nu	Wk	-	-	Rp	Wk
Mermaid	-	-	Rs	Wk	Rs	-	-
Battle Speed			16,933

Wave 3

Quetzalcoatl	Matador	White Rider

Resistances
Quetzalcoatl	Rs	Rs	-	-	Rs	Rs	Wk
Matador	Rs	-	Wk	-	-	Rs	Rs
White Rider	-	-	-	Dr	Wk	Rs	Rs
Battle Speed			23,833

Auto Party

Tested by Ronfar; loses once every 15 or so fights, depending on support demon and luck with dodging God's Bow instant kills

Speed & Support	Healer	Speed & Support	Dark DPS
Garuda	Asherah	Huang Long	Black Frost
Bufula L	Mamudodyne	War Cry	Dark Amp
Resist Ice	Null Mute	Speedster	Resist Light

Garuda is set to Support AI so it will cast Fog Breath. Garuda cannot be hurt at all by Quetzalcoatl and Quick Mediara does run out of uses, so if you kill Matador and White Rider twice and Garuda is still alive, you are guaranteed to win eventually. Matador is weak to ice and White Rider is weak to Force, the two elements this Garuda can use. My Garuda happens to have Panel 1 and half of Panel 2 filled, but it seems like it should work just fine without panels. (Resist Ice is probably unnecessary, but I use Garuda elsewhere as well.)
- Brands: Speed, Spell (Mag Atk+%, Speed+)
Asherah is also immune to Quetzalcoatl's attack spells, and Mother Creation helps if White Rider manages to inflict an instant kill. Null Mute protects her from Matador's Dark Sword skill; getting muted is a disaster and Ward brands don't always last long enough. Mamudodyne helps kill enemies - every wave has an enemy with a Dark weakness - and usually won't keep her from casting Mediarama.
- Brands: Heal, Divine (Mag Atk+%, Healing Amount+%)
Huang Long is primarily being used for 6 MP Luster Candy and War Cry rather than Five Elements; the enemies tend to fight defensively and some have attacks that ignore Five Elements completely. Garuda without Speedster isn't enough to raise Battle Speed high enough to beat 23,833, and my Yellow Huang Long was the best speedster I had available. (When I did try Purple Huang Long for Five Elements spam, I lost.)
- Brands: Ward, Divine
Black Frost's Go To Hell skill inflicts piercing Dark damage and also inflicts Curse, hitting a weakness against each wave and limiting the amount of HP that the enemies can heal.
- Brands: Ward, Divine (Mag Atk+%)

Semi Expensive

Huang Long

Skills

Mana Aid

Speedster

Brands

Life

Garuda A

Skills

Speedster

Resist Ice

Brands

Divine, Dodge

Yoshitsune

Skills

Phys Boost

Savage Glee

Brands

War

Susano-o

Skills

Force Boost

Resist Fire

Brands

Divine

Garuda A can probably be replaced with Panel 1 Garuda, though Panel 3 is optimal to have Matador miss him more often.
The purpose of Garuda A and Susano-o is to snipe White Rider who is the greatest threat to your run and happens to be weak to Force.
If you manage to consistently snipe White Rider the fight is quite trivial.
Garuda A has a second use in the fact that if Matador misses, you will debuff Evasion. It will prevent Yoshitsune to miss without needing too much accuracy on him.
Yoshitsune is replaceable by a strong demon with Mana Aid, but is still probably one of the stronger demon to use who isn't banner exclusive.

Speed Clear Auto Party

Confirmed by Reika.

Clear speeds of about 1 - 2 minutes. With enough accuracy stats, 100% clear on auto is possible.
Before attempting an auto-run, turn off "receive assists from other players" in your auto-settings, as random physical assists that miss Matador will trigger Andalucia.
If you have support demons with shaky accuracy on your friend list, consider turning off "choose support demons automatically" as missed attacks on Matador can be disastrous.
If you have enough accuracy to hit Matador consistently with your physical demons, consider running Ward brands as Dark Sword mutes can easily mess up runs.

Speed & Support	Phys DPS	Phys DPS	Dark DPS & Null Mortal
Kartikeya	Yoshitsune	Shiva_A	Yama
Offensive Cry	Great Aim	Great Aim	Dark Amp
Mana Aid	Epitome of Carnage	Butcher	Dark Boost

Kartikeya provides the battle speed required to go first, while providing your entire team additional Accuracy and Crit. The former is crucial to hit Matador, while the latter useful to fish for extra turns. Change his AI to Support so he will cast Offensive Cry - it is the strongest attack buff/debuff combo in the game and Mana Aid allows him to spam it every wave.
- Brands: Speed, Speed (Phys ATK%, Speed%)
Yoshitsune helps with the wave clear and can deal massive amount of damage to the Boss once the side mobs have been cleared. Panel 2 is highly recommended; the added mana allows him to throw multiple attack spells at the boss even with War brands. Consider inheriting Mana Gain if you do not have P2, this at least lets him use 2 spells consecutively.
- Brands: War, Ward/Aim (Phys Atk+%)
Shiva Alt in Teal drains every elemental spell the Boss can cast, while providing solid DPS for wave clear. Paired with Yoshitsune's Vorpal Blade, Third Eye can easily clear the whole wave - it is crucial to clear both waves in a single round, as Yama's Null Mortal buff does not refresh at the start of the wave. If additional accuracy is not required, Mana Aid can be used in place of Great Aim for even faster clear times.
- Brands: Divine, Ward/Aim (Mag ATK%, Accuracy%).
Yama provides a 3-turn Null Mortal buff to everyone, letting you tank God Arrows from White Rider. He also casts an AOE dark spell at the beginning of the Boss wave that has 100% curse chance - not only will this mess up the AI by making them prioritize healing, it will also reduce the amount of healing they receive. He is also a strong dark caster that will hit the Boss for weakness, netting you extra press turns.
- Brands: Divine (Mag ATK+%)