General: Always throw a Slow effect onto the boss, whether it's from a White Magic spell or a Spider Silk; it tends to make things a lot easier. Also, you should have someone put up Protect and Shell to reduce damage (bosses rarely stick to melee or magic exclusively; keeping both up will give you one less thing to worry about).
Dedicate one person to exclusive healing, and have the others focus on doing damage (if a character who can heal AND dish out punishment (Paladin Cecil, for example) can't contribute much for damage, put him/her on Item distribution/backup healing). If Cecil is a Paladin, assign him to Cover your healer (or, in some cases, caster) from melee attacks (if you have the Counter Augment, teach it to Cecil; it's a nice combo to Cover).
Magus Sisters (Cindy, Mindy, and Sandy): A tricky trio, but not very hard once you figure out the fight. Cindy can't use magic other than reviving her sisters and some sort of non-Reflectable heal (but she does have one nasty melee attack; Protect is recommended), but her sisters can: they'll put Reflect on Cindy, then bounce spells off her towards your party. Slow Cindy and put Shell up to buy yourself some time. This is the trick to the fight: You can silence Sandy and Mindy! Since they have no melee attack, Silencing them effectively takes them out of the fight. With those two disabled, have Yang, Cecil, and Cid focus on bringing Cindy down while Tellah heals through Cindy's Counterattacks. When Cindy's dead, dispose of the other two however you want.
Lugae (2nd form): The first form was easy, the second isn't. He uses a move called "Reverse Gas" on your guys, which turns healing into damage and damage into healing. He casts it randomly (so it switches between "normal" and "reversed"), so it can be tough to figure out how to time everything. It seems status moves (Shell, Protect, etc.) aren't affected by the gas; use them if you want (I highly recommend using Shell to protect yourself from his Flamethrower attack).
Make sure you have at least one Elixir handy before starting the fight: when the gas is in effect, is it on Lugae. I know what you're thinking: It's one of the dumbest ideas ever. Tell that to the 9k+ damage he takes from the Elixir! Slow him to give yourself enough time to use the Elixir.
Rubicante: You don't want his cape open, otherwise he'll blast you with that Inferno spell he used on Edge. To close his cape, have Edge use Steal on him whenever it opens; you won't get any items, but you'll protect yourself from Inferno. On the negative side, he Absorbs most Elemental damage types while the cape is closed; you'll have to rely on melee attacks and Rydia's Bio/Quake spells and Titan/Dragon Summons for damage. Have Rosa cast Slow on Rubicante, and have Cecil or Rosa put up Shell the first chance you get; he casts Fira while his cape is up, but he rarely does as an actual attack (usually it's a Counter). Even with your advantages, smash him as hard as you can; he sometimes casts Blizzara on himself (the cape Absorbs it, healing him).
Oh, and to those who played the GBA version: Rubicante's cloak affects Icebrand and Icelance this time around. Do NOT face him with those equipped on Cecil and Kain; use your strongest alternatives. Rosa should focus on healing, Edge should Yield until the cape opens (keeping him available and doing nothing is better than him attacking Rubicante just to have the cape open immediately after), Cecil and Kain should melee him (have Kain use Jump now and then, after he's been buffed), and Rydia should blast him with her Earth, Holy, and Bio spells.
Demon Wall: Make sure you buy some things for Edge to Throw before you come to the Sealed Cavern, and hold onto the Fuma Shuriken found inside.
You have to kill this thing before it reaches you, and you don't have much time to do it. As always, cast Slow immediately. Get Haste on EVERYONE, either with Hermes' Sandals or Rosa's Haste spell. Don't bother with Protect or Shell; the only damage Demon Wall inflicts is a guaranteed 1-hit KO anyway.
Use Cecil's and Kain's basic attacks (Jump takes too long), while Rydia uses Bio or her -aga spells (doesn't matter which). Edge should not use his ordinary attack; instead, spend every one of his turns using Throw on the Demon Wall (even an ordinary Shuriken does more than his normal attack). Rosa, however, is pretty much useless after the Demon Wall is Slowed and everyone has Haste; there's no damage to heal, the boss only has ONE move besides his instant-kill Crush (a Counter move that afflicts the target with Petrify) and even with the best gear available at this point in the game her damage output is surpassed by those spell items (like Bomb Fragment and Arctic Wind) that are likely filling your bag. Her turns are best spent either using those items or Praying to keep everyone's MP high; if someone gets hit with Petrify, you can usually afford to leave it for a run or two before it needs to be removed, in which case have her use Esuna.