The Treasure Chamber is a place where Pit can destroy pitchers for chances to find valuable items. Each room is stocked with 8 pitchers, and it costs 5 Hearts to destroy a pitcher (with insufficient Hearts, the shot does nothing). However, the God of Poverty is hiding in one of the pitchers. If encountered before all the pitchers are destroyed, the God will prevent Pit from shooting any more pitchers. If the God is in the last one, he'll instead leave behind a rare item. Naturally, there's a trick to maximize the treasure.
All other pots will vanish if Pit collects any uncovered treasure, so he should wait until all treasures are revealed before picking anything up. If Pit uncovers the God of Poverty, he'll get booted from the room without being allowed to collect any uncovered treasures. Should Pit shoot the last jar, the God will leave behind either: Angel's Feather, Bottle, Credit Card, or a Water Barrel.
In order to make it easier to get across, we'll give the pitchers numbers, as seen in the Chamber. The God's position is dependent upon the number of Mallets found. Count the mallets obtained, check the chart below.
............... .1 2. .. .. .3 4. ... ... .5 6 . .... ... .... .7 8. ...............
In the Underworld, shoot pitchers 1, 3, and 8.
Mallets Found: 0 1 2 3
God's Position: 7 2 4 6
Mallets Found: 0 1 2 3
God's Position: 8 5 6 1
Trying to guess the God's location is more tricky in this adventure and there's no guaranteed method, but the room doesn't change dependent upon Pit's location.
............... . 1 2 . .. .. .3 4. ... 5 ... . ... . .... .... .6 7 8. ...............
Note the items that Pit finds when he shoots a pitcher:
Step 1: Shoot 5 and 7 first.
Step 2a: Obtained 1 Hammer and Heart: Go to Step 3.
Step 2b: Obtained 2 Hammers or 2 Hearts: Go to Step 4.
Step 3a: If Pitcher #5 was a Heart, the God's in Pitcher #4.
Step 3b: If Pitcher #5 was a Hammer, shoot Pitcher #4, then go to Step 5.
Step 4a: Pitchers 5 & 7 both had Hearts: The God is in either 2 or 3.
Step 4b: Pitchers 5 & 7 both had Hammers: The God's in Pitcher #8.
Step 5a: Pitcher #4 had a Heart: The God is in either 1 or 8.
Step 5b: Pitcher #4 had a Hammer: The God is in either 2 or 6.
Information used with permission from Daniel Remar's Kid Icarus guide. It can be found here.
Also, AstroBlue's Kid Icarus: Of Myths and Monsters guide, found here.