Make your way through the forest, back up the hill and enter Conde Petie. Make your way to the area where you can buy weapons and armor, talk to the dwarves that are standing in the way. Go back out and search by the corner of the stairs to get a Phoenix Pinion. Go to the inn, turn left from the entrance to find it. You should see the Priest walking along the hall, talk to him and he will to you to a place to perform the ceremony.
Choose whichever option you want when prompted, what ever your choice is you will be able to pass through the twin dwarves. The second option is a little disturbing... As Zidane and Dagger are about to head towards the ceremony, a girl and a mog rush out. Head down the path and the party will come across the little girl. Once she has fallen from the branch she tells you her name is Eiko. Eiko is now a member of your party, equip the Auto-Regen ability to her that she gets from the Golem's Flute.
Head up the slope, climb the vines to reach the chest and open it to get a Remedy. Follow the path to the right until you come to a statue, examine it and take the Blue Stone. Head back to the left and climb down the vines, go to the lower level and walk all the way to the right and into the next screen. Climb up the vine that you see and go into the last screen, open the chest to get a Tent and take the Red Stone from the statue. Climb back down the vines and continue on your way.
Proceed to the right, continue moving through the area until you run into the moogles. Talk to Stiltzkin and buy his item combo, you can save your game by talking to Suzana the moogle. You should also have a letter for her from Mogmatt back in Conde Petie. Suzana should give you a Kupo Nut for delivering the letter to her, she won't give you one if you already have one in your inventory.
Walk around the moogles and move to the left, climb up the ladder and then move across the giant root. Before going into the next area take the time to make sure that your characters are at full health and MP and that they are using good equipment. Make sure that Dagger has the Float ability, she can learn this from the Stardust Rod. Proceed across the root, when you come to the next area Zidane and the others run into an enemy, a boss battle begins.
Higigars uses an Earthquake attack to deal Earth damage to the entire party, negate the damage by casting Float on your party members. Have Eiko cast protect and Cura to heal the party. Cast Slow on Hilgigars with Vivi and cast Bio every turn to deal over 1000 damage to him. Same old with Zidane, alternate between stealing and fighting. Eiko and Dagger can summon Eidolons to deal a fair amount of damage.
Higigars may use Curaga to heal over 2000, just continue attacking him normally to take off the HP. If float and protect wear off just cast them again but if you are keeping your party healed it isn't really necessary.
When the battle is over, approach the statue and take out the Yellow Stone. Proceed to the right and follow the lower path, open the chest for an Ether and take the Green Stone from the statue. Now backtrack to the area with Suzuna the moogle, follow the path under the root and approach the statue. Place the stones and a Moonstone will come out of the back.
Proceed back up the ladder, over the root and follow the path to the right which will take you back to the world map.