Token Items.
These are extremely helpful for fighting Floor Bosses. Most of them you might be familiar with from Besieged, and the ones that are superbly helpful there are also superbly helpful here.
These cost tokens, but once you start getting the hang of succeeding, many people (especially your non disc holders) will be swimming in them and you can boost your performance greatly with these. Of note to get:
Front Liners: Fanatic's Drink is a LIFE saver when you pull hate. Think of it like an Invincible that you pay 200 tokens for. Body Boost (200 tokens) is another life saving item that takes a ton of pressure off your healers.
Finally, when you're pressed for time, especially on the 60-100 bosses, you'll want to start investing in these items to boost your melee damage over shorter periods of time. Or to pierce stupid defenses of some bosses that make things simply take longer.
Barbarian's Drink (100) : Attack up
Fighter's Drink (100) : Accuracy Up
Soldier's Drink (200): Increases Damage done to a target
Monarch's Drink (200): Grants Regain (180 TP over time, like a Meditate)
Champion's Drink (200): Grants Potency (critical hit rate up)
Dusty Wing (200): Grants 300% TP.
For earlier boss floors, where the reward #s of tokens or not so big, you can get by with just a Fanatic's Drink and/or a Body Boost. When you're getting back 1300 tokens a run, feel free to bring the kitchen sink. You'll thank yourself when you are able to take down a Hydra in 4 minutes with 30 seconds remaining on the clock and an Askar Korazin drops.
Back Line jobs
Dusty Elixir (300): Restores some HP/MP.
Mana Boost (200): 2x the MP. Great to use just before zoning up to floor 60 or 80, and resting to full.
Body Boost (200): Also good for weak mages who might pull hate or for stray AoEs like Hurricane Wing that you just have to suck up.
Oracle Drink (100): MAB up. Great for BLMs, especially on floors 20 and 40. Less effective but still good on 60-100.
Assassin's Drink (100): M. Accuracy up. Also great for BLMs, and also great for RDMs trying to stick those enfeebles. Also possibly BRDs, though Elegy is hard to get on.
Additionally, Cleric's Drinks (200) are useful for all jobs if you don't have a WHM or someone else capable of removing Status effectives, and can afford them.
At minimum, I'd say get weak Taru BLMs Body Boosts, and all front liners Fanatics and Body Boosts. Buy more and more items at higher floors. At the beginning of the run, we like to use X in party chat to signify that all the purchasing is done by that person, and when the disc holder sees 4 or 5 Xs, they go to the designated level. WHMs hold off on using Protectra and Shellra before starting the first floor, because it cancels menus and the Rune of Transfer.
Floor Bosses
In general, all bosses are vulnerable to Elemental Sealed RDM enfeebles. If you have an RDM/BLM, by all means land an ESed Slow II and things become WAY easier. Dia II lands of course 100% on all bosses, and Paralyze II is difficult to stick, but helps. Gravity doesn't work on some bosses, from what I remember. If you have more than 8-10 minutes, feel free to TP on the Rampart, killing them or avoiding them has no effect on the armor drop rates. With less than 8 minutes, you'll have to consider who the boss is and what the minimum amount of HP/MP you can rest and still have enough time to kill the boss. You want the leader additionally to be the person least likely to die, so if you don't have MP or time for Raises, you can remove dead people from the party if they can't get up to pass gear they can't use. If they need to lot, obviously you need to get them up quickly!
On floors 20 and 40, you fight Adamantoise, Behemoth and Fafnir. These are obviously weaker versions of their real-world counter parts but the same real world tactics still apply. BLMs are very effective on these three bosses, and not as effective on 60, 80, and 100.
Adamantoise: Can obnoxiously dispel all your buffs with Tortoise Song. I seem to recall Slow II and/or Gravity not landing on him. My apologies, it's been a long time since we fought them. Weapons do fantastic damage, and so does Black magic. With 4-5 minutes of time, you will easily knock this turtle back into his shell. You probably won't even need items.
Behemoth: Even easier than Adamantoise. Since he doesn't have a Dispel, your Body Boosts and Fanatics Drinks are safe. Make sure Warcry gets Dispelled. The other thing to watch out for is Thunderbolt, which stuns. If healers keep everyone at high HP you can tear apart this boss in 3 minutes.
Fafnir: Lots of Hurricane Wing AoEs. Everyone additionally has to stand on his feet and you don't want him to turn around, else he might Spike Flail you. THFs especially. As such, your mages are sucking up AoE damage. Use Baraera to mitigate some of the damage and just drill him down. This will be a bit harder on the healer's MP, so if you have the time, rest to full HP and MP before you start on him.
20 and 40 bosses are really quite easy compared to the ToAU bosses. In general, do not get hate from behind on ToAU bosses else you get hit by special TP moves. All are vulnerable to ES Slow II and Stun. However, BLMs are not as effective against these bosses--- you may want to consider swapping them out for a SMN or another job capable of dealing heavy physical damage to kill them.
Khimaira :
The baby of the TOAU bosses, but still not to be underestimated. Fulmination is locked until the floor 100 version, so don't worry about it on 60 or 80. Dreadstorm is AoE terror, best you can do is refill people's HP. Tenebrous Mist is TP-reset, and not dangerous, but can be annoying and slow down your killing. More frightening is Tourbillion, which hits for huge damage and knocks back people very far. Healers need to be aware their targets may suddenly be very far out of range and move accordingly. Keep people's HP up and you can drop this guy in 5-6 minutes easily. For Fulmination, I believe you want to Cleric's drinks or -na off Paralyze.
Cerberus:
Slightly harder than Khimaira, but you should be still relatively excited to see him. Ululation is an AoE Paralyze, so Bar-ras that are appropriate will help get them to wear off quickly. Again, don't get hate from the back. Bar-fire for Lava Spit and Sulfuric Breath; which is Fire damage. Magma Hoplon is a Blaze Spikes and Stoneskin; turn on the damage to knock the Stoneskin away; neither the spikes nor Stoneskin are Dispellable. Gates of Hades is locked until the floor 100 version. It's not lethal to Body Boosted Front liners, so keep up the damage, and provided Cerb doesn't regularly Hoplon, you should drop him in 6-7 minutes.
Hydra :
Hydra is, no exaggerations, a bitch. It has an AoE dispel in Trembling (small range) (removing your Body boosts and RRs possible), an AoE Gravity in Barofield, and Paralyze and Plague effects. Pyric Blast is Fire based and your front liners need to be promptly Viruna-ed after this move. Polar Blast is an ice-based attack and anyone paralyzed needs to be cured of this.
Most annoying is Pyric Bulwark . This is Hydra's Physical Shield and is not Dispellable. At this time your front liners are useless and probably won't be able to maintain hate. Do your best, slap a Gravity on and try not to die. As soon as the shield wears, your front liners need to UNLOAD. BLUs are excellent for this, since they can control their damage flow. Other front liners should still be whacking away at the heads in hopes of removing them or TPing on the nearby rampart so that they can hit with a WS after the shield wears. THIS MOVE ALONE WILL KEEP YOU FROM KILLING HYDRA.
Much much less annoying is Polar Bulwark, which is Magic Shield and grants full immunity from magical damage or enfeebles. When this is up, anyone capable of dealing physical damage should DO IT. Magic generally isn't greatly effective on Hydra so this only hurts on the Enfeeble and Stun side.
Polar moves are only used when the second head is still alive. Pyric moves are only used when the third head is still alive (the right most). Try very hard to cut the third head off, and keep at it. Hydra can take as long as 10 minutes (fastest to drop him is maybe 7) if it's disagreeable with Bulwarks, so don't lollygag when you arrive and see him. Get on him as soon as possible and unload damage when the appropriate shield is down. You'll want to and perhaps will need to throw everything at him, including 2 hours and all those token items.
One of the worst things that can happen is him basically opening with Pyric Bulwark. The DDs and front line can't really hold hate since they're not doing damage, and the healers have to heal large amounts of damage from the heavy hitting Hydra and AoEs. Do your best, is the best advice I can give,