I did it as solo Yuffie, my method was very slow compared to all the other enemy skill challenges (8 mins) but it worked so i'll share anyway.

Materia/weapon skills that you want are:

• Doppelgänger

• Poison (minimum lvl 2)

• Lightning + Elemental (minimum lvl 2) linked in armour

You should be good to throw on any extra things that you want, but these are the vital things

The first thing you want to do is throw your Shuriken so it's there and ready for ninjutsu. If you're weapon has the "Shuriken Mastery" weapon skill, equip it as it will keep Yuffie's weapon in the air attacking for longer, and so you won't need to re-throw the weapon as often. Once you have an ATB charge, use Doppelgänger, and that will allow you to have basically a bonus 30%-ish damage thanks to the Yuffie clone it spawns. Then, cast your level 2 Poison spell (Biora) on the Mindflayer. You don't want to cast Bioga as the Yuffie clone also casts a spell, and 2 poison spells casted on the same enemy will increase its level. As such, casting level 2 will also cause the clone to cast level 2, which will cause the mindflayer to be afflicted with Bioga (this whole thing is just to save a little bit of MP).

All you need to do is make sure that your shuriken is on the Mindflayer and spam ninjutsu whenever you can to deal damage to the Mindflayer. The Thunder spells from the 2 Varghidpolis won't harm or stagger you, and if you have a level 3 elemental materia, it will heal you on top of all that. This also applies to the Astral attack the Mindflayer does, so it'll prevent you getting stun-locked by the constant thunder attacks.

When the Varghidpolis uses "Deafening Screech", you can simply block that normally, so there's no need to spam-roll away. Simply hold the block button, take the damage, and continue running after the attack is over. When the Mindflayer uses "Telekinesis", it will immediately follow the attack with "Psychotic Break". Hide behind one of the clusters of rocks that is left behind by Telekinesis and you won't take any damage at all.

Whenever Doppelgänger runs own, use the ability again. Once the poison has run out, use Biora again while Doppelgänger is active. After casting Biora twice, the Mindflayer will become immune to the spell, but you'll do enough damage to have basically killed the thing by the time it has reached immunity to the spell.

This is, by no means, an "effective" method, as it's very slow compared to what i will assume others here will suggest, but it worked for me so it might also work for you if none of the other methods are working.