For the mean time, you can't get everything here, but you can still cross. To begin with, use Scoop on the sandy patch the dog is sniffing - it'll unearth a geyser which you can use to jump up to a ledge. Slide down the groove, hop across the gap, then climb the vines. Go left, and climb up the rest of the vines until you get to three grooves. Slide down the middle one (you can go right and use Lash on a rope if you get the wrong one). Hop over the gap and walk around to a rocky stump on the edge of the cliff. Use Move to push it into the water, then go back and use the groove to slide down. Climb down onto the rocks above the water using the vine.
To get across, go:
Left, Left, Left, Up, Up, Left, Up, Left, Left, Down, Down, Left, Up, Up, Up, Right, Right, Right, Right, Up, across the stump and to the vines. Back on solid ground, head north to some more vines. Go around to the right, then when the rocks narrow, you can hop across to the left. Go north, up the vines, and follow the cliffs around to the right to get a Sleep Bomb from the chest. Then go back down, climb down the vines and head left. Keep climbing up and ignore the long tightrope - go up the next set of vines and follow the cliffs to the right. You'll get to a junction between some vines and a path south. The vines lead to a dead end, so go south, past the puddle. If you keep going south, you can fight Kindle, the Mars Djinni to make it join you. Exchange Kindle (which will join Felix) for the other Mercury Djinni Jenna has.
If you go right to the set of vines you passed a moment ago, you can follow the path along and south to a finger of land with a red mushroom on the end - this is the Laughing Fungus. Take it, and then go all the way back left and cross the tightrope you ignored earlier. Follow the vines and the cliff southward until you can leave the cliffs to the west.
Chill, the Mercury Djinni
The path you are on now leads to a town called Naribwe, but you'll want to get another Mercury Djinni first. Follow the path north until you see a bridge to the west. Go south and follow the path across the bridge. Keep going south until you're at the very bottom of the large forest on the southern tip of Gondowan. Chill will show up in a random battle - defeat it to get it to join your party. For the mean time, leave it on standby and give it to Sheba. Now, head all the way back north, rejoin the original path, and enter the village of Naribwe.