Sphinx is a legendary Yoma, who was alive throughout the Great Monster Wars and is still alive to this day, making her one of the most ancient beings in the Paradox universe and the original timeline. She is one of the super bosses and resides within the Pyramid . She is also in the Labyrinth of Chaos, albeit in an even stronger form.
Much like in the original timeline, they traverse through the Pyramid and encounter the same mobs on the way. Key differences are that in the original trilogy, Luka was with Sara to help her pass the Trial of the Dragon Seal, which involved getting to Sphinx. This time, Luka doesn't have Sara with them, and Luka with his companions are going into the Pyramid to return Sara to her human form, which involves getting to Sphinx.
When Luka meets with Sphinx, she tells them that she has no interest in the affairs of humanity, but when they explain to her that Sphinx is the reason why this is happening, she perks up. After Sphinx explains to them that her humanity cannot be restored, Luka is distraught. But she does tell them that her sanity can be returned; by accelerating the process. Luka and Sonya are naturally confused at first, but after Sphinx describes to them that her loss of sanity is tied to her becoming a succubus so quickly (due to the Lilith Sisters), they understand.
To do this, Sphinx gives Luka a phial of her blood, tells him to have Sara drink it, and she will go back to her usual self. After working out how to get Sara to drink the blood, Sphinx tells to go away as she "likes her peace and quiet".
After this, Luka can challenge her, but, unlike Nanabi, she doesn't join party (altough, rewards for beating her are still pretty cool)
“A mixed beast monster that guards the Pyramid, believed to be older than 1,000 years old. Through her long life, she has come to wield powerful magic. Through various circumstances, she has become the judge over the [Dragon Seal Trial]; however, it seems she despairs at her role and lives her life in immersed hopelessness.
Those who fail the trial are violently raped, then eaten. She forces her prey to be entranced by pleasure as she swallows them whole and slowly digests them inside her gigantic stomach.
Her enormous magic, built up over hundreds of years, renders her all but immune to any type of sealing magic.”
- Attack-Normal Attack, One Enemy
- Demon Beast Dance-Physical Attack, Random Enemy, Lightning Attribute, Shock 10%, Attack Four Times
- Ark Obelisk-Magical Attack, Random Enemy, Fire Attribute, Burn 10%, Attack Nine Times
- Kiss of Death-Physical Debuff, One Enemy, Death 75%
- Mother Goddesses Handjob (M)-Pleasure Attack, Target:Luka
- Mother Goddesses Handjob (F)-Pleasure Attack, Target:Female
- Mouth Offering-Pleasure Attack, Target:Luka
- Isis's Lovemaking-Pleasure Attack, Target:Luka, Trance 75%
- Ancient Law of Ecstacy-Pleasure Attack with Bind, Target:Luka
Sphinx is the second easiest super boss (or the second hardest, if we're talking about super bosses who don't reside in LoC and aren't powered up versions of normal bosses). The difficulty is automatically set to Normal for this fight, making her even harder than Alice/Hades, depending on how you look at it.
She has very high defence, very high damage and very high resistances. I'd go as far as to say that she isn't supposed to be beatable in part 1, though this is probably an overstatement. NG+ mode is highly recommended though it can be done on the first playthrough with great difficulty and time. She isn't particularly weak to any of the elements so don't bother taking those into consideration unless you want to.
Evasion boosting skills and damage boosting skills are a must if you want any hope of winning this fight. So the Superstar, Wind Harpy jobs and the Seadragon Dancer race are also a must. Superstar for the damage buffs and debuffs, Wind Harpy for Sky Dance, and Seadragon Dancer for Timewarp dance to slow down/stop Sphinx, but you must also be a Time Mage to use this skill. Try bringing Sully and any harpy (Pyhar) with you to fulfil those roles. Sully has access to the Seadragon Dancer race and Time Mage job so she can increase the parties evasion while also slowing down Sphinx, while Harpies have access to the Wind Harpy race which includes Sky Dance, which provides a 50% evasion chance.
Having at least one Battlemaster is also a must, they can equip two weapons and have excellent stats overall. The Battlemaster should be Luka. Anyone else should be a Pope to provide healing throughout the fight. Finally, try making sure each party has access to the Vicarious Clara skill. Vicarious Clara can be used by reaching level 9 in the Summoner job. Vicarious Clara creates a shield which blocks three attacks and can also be stacked, making it invaluable against skills like Isis's Lovemaking which hit multiple times.
If you have all of this, then you can proceed to fight Sphinx. Start by summoning Vicarious Clara with Luka (your Battlemaster) and then start using skills like Sky Dance (Wind Harpy), Time Warp Dance (Seadragon Dancer) and most importantly, the Superstars buffs and debuffs (unable to list them). If you have these active, just summon Vicarious Clara with your other companions as it stacks. But make sure none of your evasion or damage increase buffs go down. Ever. With your Battlemaster, you should be using your Special skills which increase damage (Transform, Focused Mind, Power Charge, etc.). Once you have as many damage boosting stats active as possible and you aren't in danger of dying next turn, attack Sphinx. She should die. If not, just rinse and repeat.
Sphinx is an entirely optional boss, and you will receive no reward for beating her. All you will get is her Monsterpedia entry. It doesn't work like Nanabi where if you beat her, she will accompany you. She just congratulates you.
For a video, see the link provided (yes I know this is Chaos Labyrinth version but it works the same way. And we don't have a video for the normal version).
For a guide, see the link (yes I know this is also the Chaos Labyrinth version but the skills and items info in there is very helpful).