For this you have to obviously have to win 50 Speech challenges. This is based on the amount of Speech points you have, the higher you have the easier successes you have. There is an exploit for this you can do in Little Lamplight that involves you talking to Knock Knock. To grind this out follow the conversation below:
Start the conversation the involves her being in charge of morale.
She will tell you a joke (Its a Knock Knock Joke....)
Answer who's there.
Say Noah Who.
Lie to her and tell her it was a good joke.
Ask her to tell you a joke again.
(Rinse and repeat until the trophy pops.)