Shrine of Decay/Exploration

Unit EXP Guide
In order to gain the maximum amount of experience points possible, you must win all monster encounters available until obtaining a certain amount of gil from each of the two zones. You can open the menu to keep track of the amount of gil you obtained from the dungeon. Because the amount of gil you can collect is predetermined, it will indicate your progress in defeating all available monster encounters.

If you want to clear the map completely:
 * Stay in ZONE 1 until you have 2,163 Gil.
 * With Full Steal: 4,326 Gil.
 * Proceed to and stay in ZONE 2 until you have 5,113 Gil.
 * With Full Steal: 10,226 Gil.
 * Defeat the boss.