Taopo Swamp is an optional dungeon. You don't have to do it; the only things you get from doing it are a Venus Djinni, some forgable materials and some other random items.
Firstly, run along to the right. Move the stump off the plank towards you and watch it sink into the glop below. You're going to be wading around in that. Anyway, hop across the planks and use Whirlwind on the left-most ivy. There's a door behind, so go inside. Use Scoop to dig the Tear Stone out of the ground, then go back outside. Descend the stairs into the swamp. The air bubbles here are like platforms - every step you take in the swamp, you sink. If you sink too far you'll return to wherever you got in. Navigate the rocks using the air bubbles so you can cross to the bottom left of the swampy area, where there are some stairs.
Up them, you can find a chest containing a Cookie. Head back down into the slime, and wade your way back across to the stairs at the bottom right. Although there is a cave behind the ivy, you don't want to go in there just yet. Swap one of Felix's Venus Djinni with one of Jenna's Mars, then use Growth on the plant. Climb up, then slide down the two grooves and use Whirlwind on the ivy. Enter the cave.
Follow the path around to the right. In the room with the hot airjets, wait for the first one to stop blowing, and run past. Wait until the jets start blowing again. When the next one stops, immediately use Douse in the pit. Quickly freeze the puddle it froms with Frost, climb the ladder, and jump across. If you're not fast enough the airjet will blow again melting the pillar. Once you're across, slide down the groove and take the stairs down. Ignore the Lash rope for the mean time and head down the next pair of stairs.
You'll be in a room full of lava. Anyway, head down. You might want to set Douse to a Psynergy Shortcut. Use Douse on the burning rock and then use Move to push it into the lava to act as a platform to get around the rock.
You can't do anything to the right, so head down and through into the next cavern. Hop across the rocks to the right airjet. This bit is annoying - you have to be very very quick and anticipate when the jet is going to stop because the gap in between blasts (which will push you back down the chain of rocks) is short. You'll want to take the top path of rocks (don't try and go from the bottom of jet up to the top - you don't have enough time). Go down on to the bottom bank of the lava and hop across. Use Douse on the rock, and Move it up to form another platform. The chest that this allows you to get only contains a Vial, so you can ignore it if you want.
Go right, and use Douse on the glowing rock. Move it into the lava and it'll drift up. Jump across and head back into the first area. Now you're here, use Tremor next to the pillar with the large rock on to dislodge the rock. It'll fall of and block the lava flow, redirecting it to the left. It'll also spew out a burning rock. Head around to the burning rock, use Douse, and push it into the lava. Hop across and use the path that formed when the water met the lava, and head down the stairs. Use Douse on the glowing rock, and move it out of your way. Head out the bottom and follow the top path until you reach another room with a glowing rock.
Use Douse on this one, and use Scoop on the glowing patch of ground to get some Star Dust. This is another forgeable material. Now, Retreat to the exit of the cave.
Flower, the Venus Djinni
Now it's time to take the path you didn't take earlier. Drop down the groove and wade back down the swamp to the stairs. Use Whirlwind on the ivy here and head inside. Head down the left-hand stairs and use Cyclone on the patch of weeds to get a Bramble Seed (if you want it). Go back upstairs and time your steps past the airjets to reach the Moveable pillar. Move it across to block the airjet. Head to the right past the rocks and the blocked airjet and then north, around the path. The stairs at the top here lead down to another Tear Stone which you'll need to dig out of the ground with Scoop. Back up on the airjet floor, head around the right. You'll have to do some more timing with airjets here. If you fall off, or head down the stairs yourself, you can use Cyclone on the weeds down here to fight a Mad Plant. Defeating it gets you a Lucky Medal.
Once you get to the other side, Move the pillar to block the airjet. The jet in the area blocked by rocks is now powerful enough to push the Venus Djinni off! Go back to the grooves and drop down the one next to the groove below the airjet you just blocked. Down a floor, you can hop across and fight Flower to have it join you. This is a whole party-healing Djinni, so it's very useful. Now, use Retreat, exit the cave, and use Retreat again, and leave Taopo Swamp. Head all the way back to Yallam.
You have 2 Tear Stones and some Star Dust to forge, so if you have enough money you can do that. It doesn't matter if you don't, just make sure you forge your Star Dust first (it's generally better than Tear Stones). You might find the Comet Mace or Planet Armor is better than anything else you can get from Star Dust, and it really doesn't matter what you get from your Tear Stones, since you'll probably only end up selling it anyway. You can use the Inn or Sanctum as well if necessary. Once you're finished, go back to your boat and sail to the cluster of islands to the northeast. Get off on the beach (ignore that blue rock for the mean time, you'll be going there soon) and enter the Apojii Islands.