There are a couple of things you can do before heading to Qu's Marsh. You have another Kupo Nut in your inventory so you can bring it to the Moogle in Gizamaluke's Grotto. If you don't have a Kupo Nut in your inventory then just skip over the rest of this paragraph. Move past Qu's Marsh and follow the roots coming out of the ground until you come to the entrance to Gizamaluke's Grotto. Move through the Grotto until you come to the room with the bell in the middle. Move around the staircase and make your way to the middle of the room, head through the door to the right. Talk to Moguta and agree to give him the Kupo Nut to get an Elixir. Once you are finished move through the Grotto and back to the world map.
If you want you can go to Chocobo's Forest and play the Chocobo Hot and Cold mini-game. To learn more about this mini-game check out the side quests section. I would suggest that you eventually do this side quest, it leads to many powerful items. Bring Choco back to the forest and talk to Mene and ask him what the big secret is. You can pay him 60 Gil to dig around the area using Choco, you have the chance of digging up a chocograph that will lead you to a treasure chest. Read the instructions and follow Choco's lead to find the spot to dig up an item.
When you are done approach Qu's marsh, which is located directly between the Lindblum Dragon's Gate and Gizamaluke's Grotto. Move through the area, past Mogster and continue moving until you reach the frog pond. You find Quina here and h/she is still alive. The frog pond is probably full of frogs at this point, if you want to play the Frog Catching mini-game, leave the area and reenter it with Quina in your party then agree to let him/her catch frogs. When you are done exit this area by crossing the bridge and moving up into the next screen.
Climb up the steps to Quale's hut and head inside, talk to him and then leave the hut once he is finished talking. Exit this screen by moving to the screen to the top left, Quina will find the entrance to the Outer Continent. Head inside and move down the steps and into Fossil Roo. As you attempt to make your way through the tunnel you will be confronted by Armodullhallan who will begin to chase you, maneuver your way past the swinging blades. If Zidane gets hit by one he will fall behind and possibly have to fight the demon. Try to avoid fighting him, it isn't worth it. When you reach the end of the line you will come to a hole, while Zidane is able to jump over it Armodullallan is not, he falls into the hole and the pursuit ends.
When you have made it to safety, Lani the bounty hunter will step in and try to get Dagger's Pendant.
This battle is easy because all of Lani's attacks are directed towards Dagger. Have Quina there to use Phoenix Downs to revive Dagger when she is KO'd, you can also cast Mighty Guard if you have a spare turn. Steal from Lani with Zidane and cast Blizzara or Thundara with Vivi. You can also cast Slow with Vivi on Lani. Continue the routine of attacking and stealing until you have dealt enough damage and the battle will end.
When the battle is over Lani runs off, go through the passage and down the steps. Move towards the left, up the steps and approach the yellow flowers growing outside of the cave. Press X when the '!' appears above Zidane's head to pick up a flower. Move toward the cave entrance and Press X when the '!' appears, this will call the Gargant, Zidane will jump on and the Gargant will take you to the Excavation site. Head up the stairs behind you and talk to the man.
Move down the steps to the right and you can find Stiltzkin, talk to him and purchase his item combo. You can save your game with Mogki, he also has a letter from Kuppo that he will read with you. In the letter Kuppo mentions that he is hiding somewhere within this cavern. He can be found near the end of this level. Mogki also has a Mogshop open where you can purchase some healing items.
This next part is kind of confusing and it will be hard for me to explain in written form, so please bear with me. Move down from where Stiltzkin and Mogki are standing. Grab the yellow flowers and move towards the end of this platform and summon the Gargant. It will take you a new area, head down the passage and into the next screen. Open the chest to retrieve Fairy Earrings, then go back and summon the Gargant again. Now head back to the area with the moogles, go past the man, head up the stairs and go through the tunnel.
Pick up a yellow flower, move towards the end of the platform and call the gargant. Proceed to the end of the tunnel and flip the switch at the end, then head back and call the gargant. Go up the steps, follow the path and open the treasure chest to receive an Ether. Head back to the last screen and follow the lower path until you reach the end of the path and then flip the second switch. Go back to the first screen and call the gargant from here. and you will be back in the area with the first switch. Follow the path and flip the switch again, go back and call the gargant again.
You should be back in the area with the moogles now. Move past the moogles and into the area that you had gone in before. Pick up a yellow flower and call the gargant to be taken to a new area. You can talk to the man to buy some equipment or healing items. I forgot to mention before, you should equip the Fairy Earrings that you found to someone now so that they can learn the Level Up ability. Go up the steps to the left of the man and flip the switch, head out into the next area, pick a yellow flower and call the gargant.
Follow the path and open the chest at the end to get Lamia's Tiara. Go back into the last area and call the gargant. Head back to the switch, flip it again and then go back into the last screen. Call the gargant again to be taken to a new area. Follow the path and go into the next area, climb the vines while avoiding the stone faces that shoot out water that will push you down, if you do get knocked down just move up the path and climb up the vines again. When you make it to the platform proceed through the opening. Follow the path up and talk to the man that is mining, he will let you dig around here if you give him a potion. Except his offer and he will give you his Pickaxe.
Go up and around until you come to a wall of rocks, continue mining this spot until you hear from a moogle. Once you have hit it enough the wall will crumble and Kuppo the moogle will pop out. Kuppo has a letter for you to deliver and he also has a shop that sells the same items that the last mogshop did. You can save your game and use a tent at this time. You can continue mining if you want to, just continue moving along the wall while hitting X to mine the spots and you can get some Ore. When you are done talk to the man to give him back his pickaxe. Move through this area by exiting through the bottom right of this area. Search the bottom left corner of this area to get a Survival Belt, then go back into the last area.
Go back to the area with the vines, climb all the way up and move to the left while avoiding the statues. When you get in front of the last one quickly move past it and hop onto the ledge, press the switch and then head back down. Proceed through to the next area by exiting from the bottom right of this area. Pick up a yellow flower and call the Gargant to exit Fossil Roo.