by Crispleaf
This focuses solely on the fight itself. For guides on how to get a Star Orb or how to get to the BCNM in Fei'Yin, I will leave that up to the many FAQs on the web already out there.
The reason I'm writing about this fight is because from my own personal experience, there is a lot of bad advice out there. I honestly think some people make up their "winning" combinations because they want to sound important and they're so sure it will work that they spout it as gospel without actually trying it themselves.

I have personally died to this BCNM doing it the wrong way many, many times. So, I feel I speak with some authority when I say I've discovered the right way to do it. In fact, it's the only way I've tried that has ever worked consistently.
Who you need:
40 PLD/20 WAR - The tank.
40 MNK/20 WAR - The damage dealer.
40 RDM/20 BLM - The healer.
I will explain the job combinations that I've tried and don't work later. But for now, trust me that this combination is your most reliable, and best chance to win. Accept no substitutes! None of these jobs or sub-jobs are that obscure nor that expensive to level up to the appropriate levels.
Your very first goal should be to find two friends, and among the three of you, decide who will play which role of tank, damage dealer, and healer. If your levels are not up to par, then take a few weeks to gain some xp. It will be well worth the effort to do this right the first time, believe me.
What you will need:
TANK'S GEAR:
The paladin should have some combination of IM and Breastplate armor. While skeletons are weak to clubs and staves, and paladins can use either, you should stick with a sword and a shield. I'll explain why later. If you can get your hands on a Grudge Sword, please do so. The Enmity +1 bonus is very valuable, especially in this fight. A Divine Sword is a good backup choice for the bonus light damage it causes if you can't get a Grudge Sword.
MONK'S GEAR:
Monks should focus on solid, defensive armor for this fight. The reason being is that despite the Paladin's best efforts, you'll still occasionally get monster hate directed your way. Hand-to-hand damage devastates skeletons so it will be very interested in putting a stop to you. Be prepared to take a few hits.
HEALER'S GEAR:
The red mage should focus on gear that increases mp and mnd more than anything else. Use a Yew Wand +1 or a Chestnut Wand for the mnd bonus. If you can't afford Astral Rings, use Electrum Rings as a cheap alternative. And, of course, wear an electrum hairpin. You won't actually be fighting, nor should the monster even attack you once, if all goes as it should.
What consumables you will need:
TANK FOOD:
The paladin needs defensive food, and juice to keep mp regenrerating (the Red Mage will only have Convert, and not Refresh, for this fight). I recommend buying one Shallops Tropicale (expensive, about 6K, but well worth it) for the defensive food. It will last far longer than the time 3 BCNMs in a row will take (just don't die

MONK FOOD:
Using a Jack'o'Lantern, oddly enough, seems to work fantastic from what I've seen (greatly improves accuracy). But you could also focus on strength food instead. A Dhalmel Steak may be just the thing!

HEALER FOOD:
The Red Mage should bring food that raises magic points and mind, as well as juice to keep mp regenerating (since Refresh is a level 41 spell and you're capped at 40). Witch Stew or Mushroom Stew would work nicely. And, as with the Paladin, I recommend bringing 12 melon juices. You may also want to consider bringing 3 x-potions for after you use Convert (one for each fight), but I leave this as an option.
The enemy you face
The Skeleton's name is Ghul-I-Beaban. It will be the three of you against just him, but with a catch. Ghul-I-Beaban will ressurect himself 4 times during the fight. And you'll only have 15 minutes to kill him 5 times.
The first 3 times you fight him, he will be a Dark Knight. He can use an area blindness attack that also steals health. Like any dark knight, he can also cast Absorb spells that steal strength, dexterity, agility, vitality, mind, charisma, or intellect. He can also cast rank 1 elemental spells like Fire.
The last 2 times you fight him, he will be a black mage. His area attack now slows you instead of blinds you and it still steals your health. His black magic spells are far more dangerous this time, however. He can cast rank 1 area elemental spells, like Firaga, and rank 2 individual elemental spells, like Fire II.
Plan of attack
Before you enter the arena, eat your food and have health and mp at full levels.
Once you enter the arena, the Paladin should cast Protect 2 and Shell 2 on his or herself. The Red Mage should cast those same spells on the Monk. After doing so, take a few moments to regenerate mp by resting.
Afterwards, the paladin should lead the charge down the hall to the main chamber, Provoking the skeleton once he or she gets there. The red mage should cast Silence on the skeleton and keep re-applying it to the skeleton for the entire BCNM (within reason: if one of its incarnations is almost dead, save the mp for the next round). Afterwards, the red mage should stay as far away from the skeleton as your cure spells will allow. You don't want to get hit by the skeleton's area attack that drains health. Also, the red mage should try keeping Paralyze in effect on the skelly too. And, of course, keep the refresh effects of the melon juice constantly on.
Apart from the Silence and Paralyze enfeebles, the red mage should focus solely on keeping the paladin and monk cured. There's no need to keep either of them at maximum health, however. In fact, it's beneficial to leave their hp slightly lower than max so that the paladin has the option to heal some damage in order to generate more hate his or her way. The "Conserve MP" ablility of your black mage sub-job should help you last longer than any other subjob could, including summoner.
The Paladin, of course, should try to keep the monster focused on his or herself. Provoke, Flash, Provoke, Sentinel, Provoke, Flash, etc. while curing yourself and the monk in between as needed. Don't forget to take some melon juice after that first Flash spell, and keep drinking more when it runs out. It's vital that you keep your mp regenerated.
The monk's job is quite simple. Punch, punch, punch.

When the second skeleton appears, it's time to murder it with a Fusion skillchain (fire and light). The skillchain goes like this:
Paladin's Red Lotus Blade -> Monk's Shoulder Tackle
When you see the Fusion fireworks display, both the Paladin and the Red Mage should cast Cure 2 (not 3) on the skeleton for a double magic burst. The reason you shouldn't use Cure 3 is because both the red mage and paladin's healing magic skill cap is still too low to do full damage with a cure 3 spell, so it's a waste of mp. Cure 2 will do more damage than Fire, in case the red mage was wondering

At this point, the skeleton will try to murder the Monk. Since the skeleton should be almost dead, you can either wait it out, or the Paladin can use Cover on the monk. Paladins, make sure the monk understands how Cover works: he or she needs to stand behind you so that you are between the skeleton and the monk. It only lasts 15 seconds, but that should be enough.
For the third fight, I suggest that the Paladin uses Holy Circle. This will cause the skeleton to occasionally "be intimidated" meaning it will do nothing as if it were paralyzed. Save tp for the fourth fight.
At the fourth fight, you should again perform the Fusion skillchain and Cure 2 magic bursts. Towards the end of this fight, the red mage should be getting pretty low on mp. So be prepared to use Convert for the last round.
If the last two fights seemed to get longer, it's not that the skeleton got tougher, it's that it probably used its slowing area attack on the Paladin and Monk by now.
Fortunately, if you remembered to keep drinking your melon juice, things should be going very well by now. Skillchain at will for the last battle and play it cool and steady. If mp is getting low for both the paladin and the red mage, and the skeleton still has a lot of life left, the Monk can always switch on Hundred Fists and the Paladin can use Invincible to keep the hate off the Monk and take no damage for 30 seconds. It's better than dying

What not to wear
Or rather, it should say "what jobs not to bring." I've tried all kinds of combinations, but here's what doesn't work:
2 MONKS, 1 RDM
Theory: The two monks kill the skeleton so fast, it doesn't have enough time to do any damage. The rdm silences the skelly and keeps monks healed.
Why it fails: This fight had promise. We made it to the fourth round easy. The problem is the slow attack. During the fifth round, the monks couldn't beat up the skeleton fast enough. The skeleton, in the meantime, found it easy to slice and dice the low defense monks during this time. The red mage (that was me) ran out of mp and everyone ended up dead... the skeleton only had a fraction of health left, however.

WAR/NIN TANK, MONK, RDM
Theory: A warrior ninja with a pair of fully skilled clubs, Provoke, Defender, Warcry, Berserk, etc. could hold enough hate away from Monk to tank. Meanwhile, the lower defense of the warrior (from holding two weapons) could be made up with Utsusemi.
Why it fails: The warrior could neither hold hate, nor could he do enough damage with two clubs (although it was better damage than a blade weapon could cause). The monk ended up tanking the majority of the time, rapidly draining the red mage of mp.
PLD/WAR TANK, RED/NIN GENERALIST, WHM/BLM HEALER
Theory: Paladin holds hate, white mage heals, red mage is all things: tank, healer, damage dealer.
Why it fails: The paladin did a fine job in this fight. He did all he could. The red mage almost never drew monster hate, and so his Utsusemi went to waste. Nor could the red mage cause enough damage with swords or clubs. I was the white mage and as you might guess, I did not have nearly enough mp to last the fight. This was not unexpected. It was thought the red mage could make up for this by using Convert and taking over the healing while I rested. But this party is too inadequate to win. We either ran out of time (you only get 15 minutes to win) because we didn't do enough damage, or we simply got killed.
PLD/WAR TANK, 2 RDM NUKERS
Theory: Since skeletons are weak to healing magic, it would help to have 2 red mages focus solely on nuking Cure 2s and occasionally healing the Paladin.
Why it fails: While this was sustainable to a certain extent with Convert and melon juice and even some hi-ethers, the damage caused was too slow in coming. We could stay alive, but not while beating the 15 minute time limit. The damage dealing of a monk is essential to this fight.