HOW TO CLEAR ARGO'S REQUEST AND GET DYNE'S OUTFIT DESIGN

First of all we need to accept Argo's request and she'll ask 20 million Credits to start the quest...after that she'll ask us to find the Speaker in the Demon Cave, you can find the chest in the far right of the map, here's the location:

Once you're done go back to Argo and she'll "Install" a big speaker in your home, there you can listen to all the Voice Lines of your friends, depending on your affinity with them.

For a detailed walkthrough check the video below.