Now before you go further, let distribute some augments:

• Give Draw Attacks to Cecil; Draw Attacks and Counter is a perfect pair of augments.
• Give Fast Talker and Bluff to Rydia. I would equip Rydia with Fast Talker and Bluff immediately. Fast Talker reduce casting time, and Bluff doubles intellect for the next magic attack.

Once done, let's head to Tower of Babil. there is only one path leading to the tower. Note that this is a one time visit, so  make sure to farm all Bestiary.

Here is a bestiary checklist:

• Leshy
• Ironback
• Armadillo
• Goblin Captain
• Magma Tortoise
• Security Eye
• Chimera
• Black Lizard 
• Stone Golem
• Naga
• Evil Doll
• Flamehound
• Flame Knight
• White Mousse
• Medusa
• Mystery Egg
• Skuldier
• Steel Golem

Boss: Dr. Lugae and Barnabas
First Playthrough
Kill Barnabas first so that you can fight Barnabas-Z to complete your bestiary.
Second Playthrough
Kill Dr. Lugae first to complete your bestiary.

After defeated Barnabas-Z, you'll fight Dr. Lugae in his true form.

Boss: Dr. Lugae (true form)
He has a nasty attack called Reverse Gas, you may die multiple times if you don't know the trick.
When he use Reverse Gas, all damages become heal, and all heals become damage. During the Reverse Gas, have your characters attack each other to heal and use Cure/Cura/Curaga (any type of healing) on Dr. Lugae, when he use the Reverse Gas again, everything becomes normal.

Backtrackt to #9, but before entering, unequip everything from Yang, then use Lugae Key to open the door. After watching the cutscene, backtrack to #1 to exit the tower.

Item checklist:

• Hi-Potion (x2)
• Emergency Exit
• Ether
• Green Beret
• Icebrand
• Ice Lance
• Cat Claws
• Phoenix Down
• Killer Bow
• Antarctic Wind
• Ice Armor
• Ice Shield
• Arctic Wind
• Dry Ether