I used to have an excellent walkthrough for that game. If I remember correctly, this is what you should do.
You should see a moon to the west. If not, face west. Either way, head north. Face to the west every now and then and you'll see the moon moving across the screen. It will be higher in the sky each time you look west. When you reach the correct point, you'll see the moon at the top of the screen in the center. When you get there, head east. Turn back to the west every now and then to see that the moon is dropping. Check every so often, but keep heading east. The way I did this part, was I headed east until I could no longer see the moon. Then head back to the west until you can barely see the top of the moon. Then head back to the west just far enough for the moon to disappear completely. When you can no longer see the moon, head north again. You'll encounter an area where you have to fight a monster. While walking north, before encountering this area, you should see a light in the upper right corner. After you defeat the monster, head north until you exit the desert.
I hope this works. Just make sure you use the water you have so you don't have to start over again.
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