After contracting with Maxwell and getting the treasures from Moria, you search for Edward.
Leave Alvanista, go west across the bridge, and keep going west to find Edward's house. Knock on the door to learn where Edward went.
Southwest From Edward's House
Before you try to find Edward, go southwest from his house to find a camp where you can get a new skill for Cless/Cress.
Go east, past Alvanista, then go south until you can go east, where you will find a dock. At the dock, talk to the captain to go to Freland.
Go east from the Freland dock and go into Olive Village. After the cutscene, leave Olive Village and go east and south to reach the first oasis. Talk to the person and open the chest, which contains a Rune Bottle. There is another chest next to the southern tree that contains a Flame Mantle.
Leave the oasis and go northeast to the next oasis. Talk to the old man on the small island across the bridge, and open the chest to get a Medicine Bottle.
From there, go north and west to the final oasis. Don't talk to the person yet. First, open the chests. There is a chest visible under a tree that contains a Life Bottle. Go down from that chest to find another chest under the trees. It contains a Mental Ring. Now talk to the person and you will return to Olive Village.
Olive Village and Freland Desert
Go into the inn and talk to the innkeeper. Rest if you wish, then buy some Dark Bottles and Remedy Bottles if you don't have any. Leave the village.
When you fight the Basilisk, have Klarth/Claus use Maxwell, have Arche use Thunder Blade, have Cless/Cress use Lightning and Tiger Teeth, with Mint healing at all times. If anyone gets turned to stone, use a Remedy Bottle on them.
If you have trouble finding Basilisks, go southeast from the village and walk around the area just northeast of the southern oasis. Basilisks seem more common in this area. Use a Dark Bottle to encounter monsters more frequently.
After you have won five Basilisk Scales (which you can see in your regular inventory, not in your Key Items), go back to Olive Village and talk to the innkeeper. Stay the night.
Back to Alvanista
When you're ready, go west from Olive Village to reach the dock, and talk to the captain to set sail. Go northwest and then north, then cross the bridge to the west to reach Alvanista. Go into the castle and speak with Runeglom/Lundgrom. Rest in the inn, then speak to Runeglom/Lundgrom again to get the Royal Crest. Unequip Arche's accessories now. She will leave as soon as you exit the castle.
Make sure that you have 15 Remedy Bottles, and buy other supplies and food as needed.
Leave town, go across the eastern bridge, and go all the way south. Then go slightly west to reach another part of the continent. As soon as you arrive in the new part of the continent, if you have at least 12000 gold, go south and east to find a camp where you can buy a new skill for Cless/Cress. Then go north and west, then continue to go west to find the lake. Go to the south side of the lake to find the entrance. Go north into it to enter Ymir Forest