First, visit the Radio Station in the eastern side of Diamond City and meet the fumbling DJ you hear over the radio, Travis. Next, visit the Dugout Inn and talk to Vadim. He’ll ask you to help him stage a fight in order to boost Travis’s confidence.
Find a seat and wait in the inn until 6PM for Travis to arrive. Once he arrives, talk to Travis and convince him to stand his ground against Bull and his buddy. Once the fighting starts, make sure that you engage them barehanded. Defeat them then talk to Travis. Once he leaves, talk to Vadim again and you’ll have to convince Scarlett to see Travis.
Find Scarlett and do whatever you can to convince her. You can bribe, threaten or persuade her. Once you’ve successfully convinced her, head back to the Dugoutt Inn and talk to Yefim. After talking to him, you have to talk to Travis this time.
After that, head to the Beantown Brewery and meet up with Travis. Talk to him then when ready, head inside the brewery and find Vadim. Kill all enemies along the way, including Bull. Once done, talk to Vadim then talk to Travis to complete the quest. After a while, Travis’s on-air delivery will greatly improve and full of confidence, for your listening pleasure.