Final Fantasy III/Dragons Peak

''The Warriors of Light arrive to the city of Canaan, but they get stuck with no means to go on on their quest. Having nothing else to do, they agree to help a girl in distress, by looking for her beloved one who left town towards Dragons Peak...''

Kazus
Items in brackets can be found for free, so there's no need to buy them.

Go back to Kazus where the Curse are lifted. That also means you can now buy stuff there, after Refia leave your party for a while. Go to the Inn and speak to Cid. He want to go back to Canaan. You have to use the Airship to bring him home, so conquer the River with the Folding Canoe you received from the King to get the Airship back.

Walk to the House above the Inn (Takka's house) and enter. Cid will ask Takka to fit the Airship with a Mythril Ram to bust the Boulders which block the passage to Canaan. Exit the village and enter the airship. You will then meet Refia there again to join your Party. During talking with Refia it turn out, the others were also Orphans!

Mythril Mines
With Refia back in Party enter the mines near Takka's house. Go in the big room and check the Pillar northwest to open a secret passage. Enter it and go along the way to 2 chests (2x Mythril Swords). Exit the mine and fly now to the rock and the rock and the airship will be destroyed altogether. Walk Southeast to the village and enter it.

Canaan
Cid will then leave the party and tell you to meet King Argus in order to make a new Airship. You can continue along the quest, though you may want to buy some armor and weapons since you're in Canaan. Go to the house connected to the Inn and search the firewood (Mallet). Go left of it through a hidden passage below the lamp to the pot (Golden Needle). Talk to the girl on the bed and Luneth and Refia will then decide to find Desch for her.

In the northeast part of the city is a pond with stairs of which you can enter on water. Follow the river until you find a chest (Elixer). Walk to the armory, then walk north, to the house above. Enter and talk to Cid, then talk to Mrs. Cid. Use the Elixer on Mrs. Cid. In return Cid will tell you a secret for your help. Activate the lamp, then walk down the passageway.

Grab the 8 chests (Phoenix Down, Spell Blind, Golden Needle, 20x Iron Arrows, Great Bow, 2x Gnomish Breads and Potion). Walk down into the water and onto the small island in the southeast corner. Walk right, into the passageway and loot the chests (4000 Gil and 2x Phoenix Downs) Exit Cid's house and walk out of the village and walk to the mountain.

Dragons Peak
Walk up the path and once at the crossroads, take the lower one for a chest (Phoenix Down) and continue up the path. When you come to another crossroads, take the one to the right for a chest (Spell Aero) then return to the crossroad and take the path left. Grab the chest (Gold Needle) and then go up. Bahamut will show up and throw you in a nest. Talk there with Desch and Bahamut will show up again and fight you.

BOSS: Bahamut
''In pre-islamic Arab culture, the Bahamut is a huge, powerful and benevolent creature that supports the World on its back. Later, Christian influence turned it into a "pagan devil", Behemoth (other devils: Astaroth was the Babylonian goddess of love Ishtar; Beelzebub was the Phoenician god Baal-Zebub, i.e. "Baal the Almighty").''

You are far to weak to defeat him, so just run away. After doing do, Desch will give you the Spell Mini and join the party. You will end up in a new area.

NES differences
Just some items can be different, therefore, here's a full checklist: