Note - Conditional Treasures: Some of the treasures listed below will not appear under certain circumstances. Below, we will cover their locations for the sake of those who did do what was necessary to get them, but not everyone will get them. In any case, if you did not do the mission "Shave the Hypello?" in Chapter 1 - Moonflow, then you can not get the Enterprise item.
Once you have returned to the Celsius, speak with Shinra and tell him "Sure" during the conversation to earn another Al Bhed Primer . Then speak with Brother as well before heading into the Engine Room - there, you’ll find four new chests: five Phoenix Downs , two Ethers , four Remedies , and eight Potions . Head to the Cabin next and speak with Barkeep and opt to rest - another 100% requirement as mentioned in Chapter 1.
After the nap, return to the hallway with the musicians (if they are there) and speak with the fat one. Push them into the elevator and you should get the Enterprise accessory. Clearly, if you did not do the quest properly in the Chapter 1 Moonflow area, you won’t be able to do this.
After the scenes and upon Yuna’s awakening, head to the bridge and tell Brother that you’ve made your decision. Two new Hotspots will appear on the map: Mushroom Rock and Bevelle.