@19:55 This is a "pit of 100 trials" You have 100 levels of enemies. It gets more difficult the deeper you go. Every 10th floor has an exit. You can get some exclusive items. SPOILERS!!! The last floor has a hidden boss fight
After chapter 4, you can do the quest "The elusive badge." This will unlock the hidden partner. Feel free to check the trouble center in Eastern Rougeport