Luka is poor and has decided to do this quest for Amira in exchange for the information needs. Alternatively, he paid for the information but he spoke to Amira in the Pocket Castle after recruiting her and now he is doing this quest as a favor for her. Either way, Luka has to stop the trafficking of Phoenix Tails coming out from the Nameless Slums.
2: After making it through the tunnel, head south to the Nameless Slums. Enter it and the group will decide to search for information on Don Dahlia by talking to people or just looking for her.
3: Go to the bar at the North East part of town. In the bar, at the farthest end is a hooded man. He'll sell you information on where you can buy Phoenix Tails and a code word to use.
5: Go to the tent on the North East part of town and say the code word to the woman inside who will reveal herself to be Don Dahlia. Finish the conversation and leave the tent.
6: Head to the south east part of town and there is a locked building. Clicking on the building plays a short cut scene where Don Dahlia enters it. If you have Ilias with you, she'll have already stolen the key from Don Dahlia after completing step 5 so skip step 7. Otherwise, proceed to step 7 with Alice.
7: Head back to the bar and talk to the third last person on the end of the bar, the blue haired man with the green cape. He'll steal the key for you.
8: Return to the locked building and enter it. A boss fight occurs and once you're done the smuggling operation is over.
9: Return to Amira.