The Garamsythe Waterway
Save at the Crystal if you like. Once you reach the bottom of the stairs, Balthier will give a more in-depth tutorial on Gambits. Examine the Fallen Soldiers for a short cutscene, then move on.
Turn left at the fork, and nab the Garamsythe Waterway Map out of the urn. Feel free to grab any chests that appear, and make your way to the next area.
The path is pretty linear, but be sure to explore all the nooks and crannies for possible chests. When you reach the East Sluice Control, there will be a Save Crystal. Be sure to use it before descending the stairs.
You'll have a short cut scene introducing a young woman, followed by a battle. You can't control her actions, so I suggest you target whichever soldier she is to make the battle shorter. Unless you messed with the Gambits, Balthier and Fran should both target the Party Leader's target.
After the battle, the woman will introduce herself as "Amalia" and join your party as a guest, meaning you still can't control her actions, but you'll at least be able to see her stats.
Go ahead and run back up to the Save Crystal, because you'll be facing another battle in the next room.
The four Flans are the hardest battle you've faced yet, but you can handle them. Amalia has Libra, so you can see that they are weak to Fire... which Fran has handy for you. Open the Gambit menu, and change her primary from attacking the Party Leader's target to casting Fire on it, and they'll go down in no time.
The Flans will also cast blind on you, which can be easily dispelled by eye drops. After the battle, I would suggest going back to the Save Crystal to heal the party and dispel any status effects. Collect the chests in the Flan Room, and move on. Don't forget to change Fran's Gambits back to Attack. For the next fight, you'll be sorry if you don't.
In the next section, there will be a D-shaped corridor. If there is a chest there, it has a chance to drop a Gambit- Foe: Targeting Self. Be sure to pick that up, but if it doesn't appear, don't worry. There will be other chances to grab it.
The next room is conspicuously empty, except for a Save Crystal. This is the game's way of letting you know that this next battle will be a tough one. Once you're ready, examine the Overflow Cloaca on the north wall.
This guy is surprisingly tough, and I suggest having Vaan almost exclusively heal. Amalia will use a Phoenix Down on anyone who falls in battle, and she'll throw a few Potions out too, but it won't be enough to balance out the damage without a little help. Keep Vaan in motion to keep your MP up, and use Cure every turn on whoever needs it most, but your primary concern should be Amalia since she'll also heal.
The majority of Firemane's attacks are simple melee attacks, and it has a tendency to teleport around the room. When it does, you may have to keep Fran and Balthier on task, or else they'll just stop attacking. Every so often, it'll use its most powerful attack: Bushfire. This attack causes a significant amount of damage to the entire party, and has a chance to inflict Poison. Spread out the item using duty to keep everyone standing.
After the battle, you'll have another cutscene, then find yourself in the next area...