As soon as you enter, get the chest immediately to your left containing a Potion, and continue further to get a Silk Web. Go further south through a gap between the walls and continue until you get a Tent and another Potion. Return through the gap and head right instead of going up the stairs. Go underneath the bridge to get another Potion. Go right and up the stairs to get a Soft. After that, go south into the next room.
Keep going down and pick up the Notus on the way, before entering the room on the left containing a Lamia Harp for Edward. Continue on, and when you see the door, go behind it to get an HrGlass1. Go back and head left over the bridge to get a Silk Web. Return to the door you ignored earlier and go through it to reach a save point and three treasure chests containing a Life, an Ether1 and an Exit. Return back to B2F and go west and south down the stairs and continue south through the door. Go down all the stairs and Edward will try and take the Sand Ruby, but the Antlion will appear and fight you.
Antlion:
The Antlion has a powerful counter attack, so hit it hard with Cecil and summon Chocobo with Rydia. Edward is pretty useless in this battle, so Parry or Heal with him. The Antlion should go down easily.
After winning, you will receive the SandRuby. Cecil and Edward will talk, and then you will be in control again. Leave the dungeon; either by walking out or using the Exit item you obtained earlier. Once out, use the hovercraft to return to Damcyan and heal. After doing so, head southwest of Damcyan to get to a bunch of shallows, which you can go over to return to Kaipo.