Flying Underground
Simple obvious tip: When you get the Luca Key, use it immediately for item space. Who knows how much space you will need...
Optional recommendations: Do the Sylph's Cave first, then the Land of Summoned Monsters, then finally the Sealed Cave. The game originally intended for you do play it in that order... and it's still a pretty damn good order. Skip to the Trap Door section if you wish.
Sylph's Cave
Fear The Monsters: The Molbol is still the most annoying monster alive, and with the increased HP, you will have a tough time trying to take it down swinging... however, there is a small trick to blocking its strongest attack.... however, this attack pales in comparison to the Ghost. It is similar to its predecssors, possessing the evil Count attack. Unlike its breathern, that's his first attack. Compare this to the Fataleye, Ghosts come in vastly bigger groups, thus making this threat significantly bigger.
In the depths of this cave, the Avenger Sword got a nice beefy upgrade... even if it is two handed. Making Kain or James an automatic killing machine is priceless. The boomerang also found here is also beefed up, arguably stronger than many of the other weapons available and with Cipher gaining uber levels and attack power, this can only be an awesome bonus.
Land of Summoned Monsters
The summoners now bring a number of familiar faces with some new ones. This is the best chance to get the Bomb summon as it may become useful, when the Mist Dragon is not your preferred option (there's a few rare instances...)
There are rumors of XT... hiding in some treasure chest.
In the town, you will find the best magic equipment... particularly with the armor. It is not a bad thing to have high magic defense...
* Bosses: Asura and Leviathan behave more or less the same, and really aren't a threat.
Trap Doors Suck
If you order your characters properly, you can maximize their AGI to their full potential. With that said, the Avenger Sword is your best bet to kill Trap Doors before they kill you. In fact, the Avenger Sword is a beast in the Sealed Cave.
* Bosses: High defense doesn't stop Berserk (status) from being a very viable option... additionally with good magic support, you should be fine. However, it is hard to fear the gradual petrification attack in response to magic...
Big Whale and Awesome Optional Stuff
I have a recommended order when it comes to getting all the optional stuff in one go. This is for people who forget about this.
1) Get Big Whale
2) Get Enterprise and Hovercraft and trade... and it is worthwhile
3) Talk to Yang's Wife - this assumes you did manage to find Yang...
4) Goto Baron to get Odin - of course, you needed to have completely done the Land of Summoned Monsters sidequest
5) Go into the underground, and give the blacksmith what he needs.. after getting what he needs, talk to him again (Step 1 is a requirement for this step to execute properly.
6) Visit Yang at Sylph's Cave - you will need this summon, as it was just as useful in the original game
7) Talk to Yang's Wife again - the item you get in return can be equipped now.. except it isn't as powerful, but it is at least useful.. when you need it
Old Man on the Moon
The only shop on the moon provides the most productive weapon for Rydia while doing the Giant... I wish Fusoya could equip it too...

Fear the Monsters: You may find yourself in pain during this trek to meet the Lunarian. Remember those parasitic creatures that loved to poison you? Well they suck at you more... literally. Its base attack is to drain you. Occasionally, it may Charm+Berserk a character in one hit. This is a very nasty combination.
You will meet Xlom, a "slightly better" Tella. That low HP and defense is ultimately the death of him. However, his retweaked MP will be more than enough to make him useful. The spell list has been reduced, but just enough since you would usually not use half of either Black+White Magic spells. You do have a number of options to make the guy better... Bow+Arrows will make him suck less in the Giant... he can equip a number of the lighter power equipment in addition to his wizard equipment.. but that's usually not something to worry about.
Bahamut's Cave
Feel free to skip this or complete this before getting Xlom. Every chest containing a Genji piece of equipment is filled with monsters and with good reason. This place truly isn't for newbies.
Fear the Monsters: The monster you normally see the most frequently may be your undoing. Take advantage of all possible weaknesses or you don't get very far. The revamped Behemoth is tougher to beat... but the most important aspect is the vastly better drops it has...
* Boss: I wonder if Bahamut could do some hurting while doing his countdown. He doesn't live long enough to matter.
Giant Headache
Take full advantage of the Mech attribute, as it makes your progress much easier. However, there is still one monster that isn't a Mech, and will proceed to annihilate you if you wait.
* Boss: The elementals are beefed up, but suffer from the same weaknesses.
Boss: The core isn't very threatening, which is good. The problem is that the healing is far far stronger than you remember it. You essentially have two options:
1) Go crazy... if you think you have the balls to face the devastation of virtual insta-death.. then go ballistic with Bahamut and the like. Reviving is essential, healing is optional and usually not recommended. You will be lucky if all your characters survive.
2) Be creative. If you know how to kill a Behemoth with low levels, then you need to do the reverse of that... (I'm not giving the entire hint). The suggestion here is to use Haste+Slow whenever possible as the extra speed will prove vital in doing damage efficiently. Sylph is
very useful here for healing.. and Bomb if Rydia's current HP is high..