Sphinx/Labyrinth of Chaos

Sphinx (スフィンクス娘, Sufinkusu Musume) is a legendary youma who fought in Great Monster Wars making her one of the most ancient beings in the world.

Biography
Like the other bosses of the Labyrinth of Chaos, you can’t talk to her; there is no rape scene upon being beaten by her, and you shouldn’t be able to beat her. This Sphinx is just a copy of the one who fought in the Great Monster Wars.

Attacks

 * Attack – One Foe, Physical, Physical Attribute
 * Beast Rampage – 4 Random Foes, Physical, Physical/Lightning Attribute, Shock 10%
 * Hades Blast – All Foes, Physical, Physical Attribute, Death 25%, 3 Turns Cooldown
 * Arc Obelisk – 9 Random Foes, Magical, Fire Attribute, Burn 10%, 36 MP
 * Freezing Polar Cyclone – All Foes, Magical, Wind/Ice Attribute, Freeze 10%, 20 MP
 * Black Lightning – All Foes, Magical, Lightning Attribute, Shock 10%, 20 MP
 * Solar Eclipse – All Foes, Magical, Bio Attribute, Mini/Petrify 50%
 * Final Demon Eyes – All Foes, Magical, Poison/Blind/Silence 50%, Confusion/Sleep/Paralysis 25%, 15 MP
 * Kiss of Death – One Foe, Physical, Death 75%, Only Targets Females (except Luka)
 * Hand of the Earth Mother (M) – One Foe (M), Pleasure Attribute, Targets Luka
 * Hand of the Earth Mother (F) – One Foe (F), Pleasure Attribute, Targets Females
 * Mouth Offering – One Foe, Physical, Pleasure Attribute, Targets Luka
 * Isis’ Lovemaking – One Foe, Physical, Pleasure Attribute, Trance 75%, Targets Luka
 * Ancient Law of Ecstasy – One Foe (3x), Physical, Pleasure Attribute, Targets Luka
 * Bestial Howl – Self Buff, +200% Accuracy (5 Turns), +50% Physical Evasion (3 Turns)
 * Disruptive Wave – All Foes, Auto-Hit, Dispel, 5 Turns Cooldown

Strategy
In the Labyrinth of Chaos, she can be fought as a super boss. You shouldn’t be able to beat her in Part 1 (like the rest of the super bosses), but it can be done. Through grinding and exploiting a skill called Vicarious Clara (Necromancer Level 8) which provides the user with a shield which absorbs three hits that can be stacked infinitely.

Fight her like you would any of the Labyrinth super bosses. However, you want to take some other things into account:
 * All her attacks can be evaded so Physical/Magical Evasion is highly effective, but she can buff her Hit-Rate high enough to hit regardless and you cannot always dispel it before she attacks.
 * She possesses multiple attacks that can be reflected dealing damage to the point of it being a viable winning strategy though it will take a while.

Check here and here for detailed information on all the super bosses and everything you can make use of to defeat them.

A battle against her with only Part 1 equipment, no Crisis Hairpin and no stats upgraded can be seen in this video.