To get to fight the Money-Money Boss in Terrace Cave, you must first get the Money enemies to use the "steal and heal" skill on your party.
To do that, you must beforehand make sure to talk to Scatterbrained Khudol in the Casino gambler's hideout in GohtzaLow Town (he's facing the right wall), he will tell you about the boss of the Moneys. Then go to The Great Ancient Ruins and run around until you encounter a party of Moneys which are found in Astral Square. Injure them enough so that they use "steal and heal" on you, be sure to kill them only after that.
Now, back to the Terrace - Cave, and you will see blinking items on the floor. They are only worth one gold each, but follow them to where you will eventually find a chest that when opened initiates the battle with Money-Money. The Biography of Backyard is the reward for his defeat. If the fight goes on too long, there is a good chance that he will flee, so it would be wise to save the game before attempting this.
If he does flee, a new gold trail appears. If you follow this, you will come to another treasure chest, where you can fight him again. This second chest is to the southwest of the first. If he manages to flee again, he will reappear back in the first chest.