Trial Road has eight puzzles in total, but you only attempt four of them, depending on the path you took. Since you only get Potions and Vials from the chests, and you can get them another time when you aren't pressured, ignore them.
The Left Path
Puzzle 1: Sand Waterfall
This one is easy. You can either run up the waterfall, get off to the right, and go across the rope to the door, or use Sand to climb the waterfall, and then Whirlwind the ivy to uncover a ladder. Both ways take roughly the same amount of time, but remember that Moapa doesn't move whilst you're using Psynergy, so the latter may actually be faster.
Puzzle 2: Log Pushing
Push the horizontal log up, then the bottom left log to the left. Climb up and around the vines, then Move the pillar into its gap. Push the horizontal log down, go around, and push the top left log across into the water. Jump across and climb the vines to the next door.
Puzzle 3: Vine Pillars
You can actually ignore the vine-covered pillars; just push the free left pillar right, the middle pillar down, and the right pillar left, then climb the vines and use the pillars to jump across to the door.
Puzzle 4: Geysers
Push the pillar up two spaces, then use the geysers as stepping stones, along with the pillar, to get across to the next door. This can be time consuming, so you will want to have built up a big-enough lead so you don't get to the last door second. Or you can go around the pillar and use Scoop on the right-most crack on the ground. this will create a geyser that pushes you up a few steps from the door.
The Right Path
Puzzle 1: Pound Pillars
For this one, Pound both the pillars that are up, then move the ordinary pillars onto the ones that are down, then jump across to the door.
Puzzle 2: Pillar Pushing
Simple; just push the left pillar up until it's one push from the top of its groove, then the middle-right pillar all the way up. Jump across to the door.
Puzzle 3: Burst Pillars
Another simple one; use Burst on the right-hand pillar and jump up to the vines. Go up to the door.
Puzzle 4: Fire and Ice
Quite tricky. Push the two pillars all the way up to the top, then use the torch to melt the left-hand ice pillar. Jump over, then climb up and jump across the pillars to the exit.
From the two, you'll find the left path a lot easier and quicker. If you have them, Brilliant Circlet, Spirit Gloves, Crown of Glory and Floating Hat are probably the best items to sacrifice, partially because PP regeneration isn't going to be much of a help in the coming fight.
Before you jump across at the summit into the marked circle, make sure you've switched all Djinn back to their respective characters. If you want, all Jupiter Djinn and 4 Mercury may be on standby. Save, then jump across to start the fight.
Boss Battle: Moapa and the Knights
This battle operates in a very similar way to Briggs and the Sea Fighters - the only major differences are that these guys are loads more powerful, use a lot of attack items, and can't summon any more of themselves.
If you did standby those Djinn, the first turn should be able to go Odyssey on Moapa, Serpent Fume on Moapa, Eclipse, Eclipse. As with the battle with Briggs, focus all attacks on Moapa until he goes down. You may want to keep all Djinn set and slowly build up Djinn over the course of the battle, since you will be constantly pounded by 100 damage item attacks (Bramble Seed, Crystal Powder, Oil Drop, Weasel's Claw). You may also get a reminder of the Poseidon battle where Felix has to sacrifice his turns and PP to repeatedly cast Revive.
As long as you get the occasional summon in, and everyone stays alive, you should be able to hold out long enough for Moapa to fall. Then, blitz the two soldiers (if they are still standing) with Psynergies or a summon rush. And don't forget Shade - Piers' barrier Djinni will save you from a lot of damage if employed at the right time.
Once they're dead, you'll rest back at Shaman Village, and you'll have the Hover Jade. Equip this on Sheba. Go to the two-floor house on the right-hand side of the village, and go upstairs. Go round to the next area to the right, and Move the pillar off. Go back to Moapa's house, go downstairs, and outside use Lash. Follow the path around the cliff to reach Aroma, the Jupiter Djinni! It'll join without a fight.
You can sell some of your junk in the all-purpose shop, now its open, and you can also get a Lucky Pepper from the jar to the right of the fortune-teller's tent (he's in the area to the right, and he'll give you a free fortune-telling as well).
To Jupiter Lighthouse
If you absolutely want, you can go all the way back to Trial Road and raid the caves for the Potions and Vials you missed. You will have also noticed a glowing purple spot at the summit (you will see these a lot in Jupiter Lighthouse - these are Hover Pads) but it leads to a dead end for the mean time.
Leave Shaman Village once you're rested and go back through Shaman Village Cave. You still can't do anything here, so just return to your boat. Sail back down all the way to Atteka. On the eastern coast there's a river between two beaches which you should sail up. You can navigate the rivers to get inside the bit of coast that's surrounded by rocky spires, and from there, into the thick river and into Atteka Inlet.