On the Boat
When you first arrive here, head up onto the boat. You'll see a scene where Briggs' henchmen are trying to get the stuff off the mast (this serves as a guideline to what you need to do once you've beaten Briggs). If you're not healed (there's no real reason why you shouldn't be), heal, equip whatever you need, then go into the ship via the door at the top. Follow the stairs down. At the bottom, don't go down yet; save your game and put Felix's Iron, Jenna's Fog and Sour, and Sheba's Breath and Ether on Standby, then go down to trigger a scene with Briggs. Jenna will speak a little too loud, and before you know it, you've got a standoff. You ask him to attest to Piers' innocence, and when he doesn't....
Boss Battle: Briggs and Sea Fighters
Since you set those Djinn on standby before, you're ready to start the battle. By now you should be around level 13, and Felix should know Ragnarok. So, for the first turn, Felix should cast Ragnarok, Jenna should summon Nereid, and Sheba should summon Flora. Focus all the attacks on Briggs. Next turn, Ragnarok, unleash Cannon, unleash Blitz. Basically, just use Psynergy and Djinn unleashes until you can summon, then summon away. Once Briggs falls, the Sea Fighters are easy to finish off (some of them will die during the battle from summons and Psynergy anyway).
Once Briggs is down and out, he'll promise to say that Piers isn't a Champa (one of him). After the lengthy talk about what's going to happen, in-between the banter of the Mayors of Alhafra and Madra, and Briggs' wife, Chaucha making a surprise entrance, you can leave. Don't head upstairs however - go back to the back of the boat and Move the large crate out of the way. In the small room, use Tremor (the Tremor Bit should be equipped to Felix) to dislodge the box with the bread on top. Pick up the bread and exit. Now, back on top of the boat, you can help the repairs.
Repairing the Boat
Firstly, Move the sandbag underneath the log to the right along until it falls into the water. Hop around and shove the log off, too. Get on the mast and walk down to the bottom. Shove this sandbag off, and then use Move to drop the crate off the sail into the water. Go back up the mast, and onto the boat again. Descend the rope leading onto the log you pushed off earlier, and use it to hop around to the bit of land on the right-hand side. Move the large crate here one space to the left, then go back to the boat. Get on the mast, go to the bottom, but this time go up. At the rope on the top end, walk along it and jump back onto the prow of the boat, past the cabin. Use Lash on the rope at the top, climb across, and descend down the vines. Pound the pillar down here and jump across. Move the crate here into the water, and jump up to the large rock. You can't actually do anything with it yet, but Jenna will say how she has no idea how to get rid of it. Go back onto the boat and attempt to leave. After the scene, head back to Alhafra. When you reach the boy crying by the stairs, talk to him, and give up the Large Bread.
He'll get better, and thank you. The cave near the Mayor's house was originally blocked off by the kid's dad, but since you gave him something to eat he'll let you pass. Now, he'll tell you not to touch any of the Mayor's treasure, but we're going to loot him anyway. Anyway, whilst on the way up to the cave from the harbour, check the hexagon of gravestones with Reveal to get a chest with a Psy Crystal in it.
Anyway, inside the cave, follow the path southwards. Pound the pillar out of the way, descend the ladder and use Lash to get to the three chests. You get a Lucky Medal, 123 coins and Ixion Mail (equip this on Felix). Go back out of the cave and go up to the Mayor's house. Inside, keep going and talk to the Mayor. Nothing happens no matter what you say. You can talk to the Madran Mayor and the Town Elder in the left-hand room to prove how much of a so-an-so the Alhafran Mayor is (he'll get even worse later on), but otherwise leave the palace and leave Alhafra (make sure to rest at the Inn if you haven't already done so).
Osenia Cavern and Spark, the Mars Djinni
Now, you can't leave Osenia to the west since the bridge is still out (this is why you had to go through Yampi Desert in the first place). But there's still some stuff to the south of Osenia that you'll want, so take that one-way exit south out of Yampi Desert that goes to Air's Rock (the cave along the way has a hidden Psynergy Stone in it which you can get with Reveal). On the world map again, go straight past Air's Rock and all the way in between the rivers back to Mikasalla. When you get there, don't enter it - instead go northeast to a dark green patch. You'll see a cave. If you went in here earlier you would have realised there's absolutely nothing you could have done, but now you can go around to the X and use Scoop on it. Climb down the ladder and back up the other one. Go up to the combo tablet to get Magaera! Magaera requires 1 Mars and 1 Jupiter Djinni to summon and will raise your party's Attack (although her attack on your foes isn't that powerful).
Now, head back to Mikasalla. Rest in the inn, then set Scoop to a Psynergy Shortcut (preferably not the one with Move in - you'll want to keep Move as a shortcut for the duration of the game since it saves a lot of time). Dig around in the sand to the bottom-left of the village (where the chicken is) to uncover a ladder. Follow the cave through and exit the other side to get Spark, the Mars Djinni! Give either Sour or Fog to Felix, and give Spark to Jenna.
Once you've done that, go back through the cave and leave Mikasalla. Head all the way back north to Osenia Cliffs, and go across.
Madra's Been Under Attack...Again
When you get back to Madra, you'll hear from the town guards that Madra has been attacked again. Not by the Champa, by the Kimbombo (who?). No-one got hurt, and only a black orb was stolen. But of course, that black orb is the key to the ship you'll be using, so you're going to have to pursue them all the way back to their secluded little town on Gondowan to get it back.
You can inspect stuff and talk to people again, but otherwise leave Madra. Now, go west, past where you got Iron, until you reach Gondowan Cliffs.