I'm going to suggest a completely different set of strategies for this (I've done it with just one other person helping - me as mnk/rdm at 26, other person as blm/nin at 25).
Note for all of these setups: All party members should have appropriate food (pie & juice for all mages, fishkabob and au lait for melee damage dealers - keeping defense/HP up is more important than an extra 3-5 damage a hit here). I recommend monks for damage dealers just because of Dodge - you WILL get aggro as a monk here, and if you get hit less often, that's good.
With 6 people: recommended average level is 18+.
Party should have two monks (DRK will work well also), two black mages, and two red/white mages. Split into two equal groups, and each group of three whales on target of choice, red/white mages healing as necessary (cure after EACH HIT).
With 5 people: 20+.
Same as above, but the damage dealer pool is now down to three: mnk/drk/blm. One of the healers should be a rdm, and will run through Dia/Paralyze/Slow at the beginning on the dragon. The monk should stick to the dragon at first; the dark knight's job is to move the eye close enough to the dragon so that the black mage can spam AoE spells.
With 4 people: 22+.
At this point, your subjobs become very important if you want to get this done quickly. The team should have two blinktanks available, along with two decent damage dealers. The damage dealers should, as soon as they get up to the platform, throw their 2hrs and take full advantage of the effect, while the blinktanks should do anything and everything they can to pull aggro back to themselves (chain-casting, Provoke [for nin/war], etc.).
With 3 people: 24+.
Recommended party for this is rdm/(blm or smn), (blm or rng)/nin, mnk/(rdm or whm).
- Monk heads in, engages dragon, throws 2hr + Dodge, and heals self as necessary (cast Cure after EACH MISS by the dragon unless at 90% HP or higher).
- Red mage waits five seconds, throws Gravity, Dia, Paralyze, and Slow on the dragon, then casts Blink and engages the eye.
- Damage dealer uses Utsusemi, then starts unloading on the eye without using 2hr.
- Whenever Blink/Utsusemi wears off, the other person working on the eye will grab aggro as quickly as possible and give the person who needs to recast a chance to.
- The red mage should have a maxed Archery skill to help with grabbing aggro off the black mage or ranger.
With 2 people: At cap.
For this fight, if possible, both members should have a juice, an Au Lait, and the recommended food item ready to use right before the fight.
Recommended job pairing is mnk/rdm and (blm or rng)/nin, although other combinations should work.
ONE OF THE PEOPLE MUST BE A MONK, AND SHOULD BE ABLE TO ENFEEBLE LIBERALLY. The reason for this is that there is absolutely NO room for error in this version of the fight, as the people will each be, essentially, soloing one of the monsters.
Both people should use their food/drink items as soon as they actually enter the battlefield, and the person capable of Blink/Utsusemi-ing themself should do so. The Monk should throw Focus + Dodge here, then run up, throw Dia (and Paralyze, preferably - do Paralyze first, though) on the dragon, and then use their 2hr. At the same time, as soon as the other person finishes casting, they should do whatever they can to grab the eye, and if they happen to be a red/black mage, should also throw their 2hr and proceed to chain-cast anything and everything that deals damage onto the eye.
If the Monk is properly equipped, they should finish off the dragon not long after Hundred Fists wears off, and can then move on to helping out on the eye (your teammate, even if they really know what they're doing, should not have finished it off yet - the eye has almost as much HP as the dragon does, and unless your buddy's a ranger, he's going to discover that the eye doesn't take quite as much damage as it should from spells).
Solo: Not recommended.
This could theoretically be done by a blm/rdm, if you can get Barsleep to actually work (the eye WILL try to Sleep you, IIRC), and if you can successfully Sleep both targets for long periods of time - however, you'd have to Aspir/Drain like crazy, avoid all of your DoTs, and use any AoEs you can. So I'm not about to recommend this, unless you really think you can pull it off. (As far as doing it as bst/* - I dunno if you can charm the eye and make it attack the dragon.)