You receive this quest automatically at the beginning of the game. Later, after Heileen encounters the ship's cat, she causes a ruckus. Otto and Lora show up and Lora offers to help clean up Heileen's cabin.

And why does she want to clean my cabin?
Response: I'm eighteen. I'm not a child anymore, Lora.

Lora will then reminisce about her scandalous youth, drawing the attention of the crew and flustering Otto.

When Heileen first boards the ship she sees John and Marco talking. To obtain the quest, she must eavesdrop on them.

In the distance, John is talking with a funny-looking man who appears to be a cook.
Response: Eavesdrop

During the encounter with the ship's cat, use these responses.

Captain Adam dismisses himself, making a slight bow with his head.
Response: "So"? It's a black cat...

Marie: You don't believe all that superstition about witches and black cats, do you?
Response: Ignorant? How rude...

Marie will take comfort by petting the cat and John will show up, referring to Heileen as "clear eyes".

Heileen's first night on the ship is disturbed by someone knocking on her door. To obtain this quest, ignore the visitor.

< knock knock > Huh? Someone's knocking at my cabin door. I wonder who it could be?
Response: Go back to bed and ignore it

She will then hear a conversation between Otto and Lora through the thin wall. The quest will be solved the next night when Heileen listens in again.

Marie will come get Heileen for the first meal on the ship. She boasts about how well she's gotten to know some of the crew.

She watches me to see my reaction.
Response: That's good... What did you talk about?

Marie: Because of how close I am to John?
Response: I'm sure John loves me, anyway.

After the meal and watching the crew arm-wrestle, the girls step outside and Marie admits that John probably doesn't like her.

The second night in Heileen's cabin, she realizes that Otto and Lora have smuggled someone onto the ship.

This will be resolved later, after Lora reveals the plan to bring the stowaways to the New World.

This quest is automatically obtained one day when Marie tells you about something she overheard. It's the word "Ebele". Later that night you'll have to use these responses at the party. This is the quest that is most likely to fail due to the specific chain of responses that must be followed.

Marie: So... What should we do?
Response: Let's split... Maybe alone we'll make more friends.

He shows me an elegant gold chalice with rum inside.
Response: Well... Okay... Just a little!

Elias: Why didn't you tell me?
Response: I'm sorry, I... I just did it so I could be more "adult."

Elias: Do you want to come with me? My cabin is just near the small library in the hall.
Response: Yes, of course.

Elias then makes advances towards Heileen, but gets thwarted. Heileen exchanges her silence about the incident for information about "Ebele".

After another incident with Marie, she will challenge you not to talk to her for the rest of the day.

As long as you choose to spend the day with Lora or other members of the crew, you will be able to avoid Marie.

Marie theorizes that Otto is smuggling slaves. This quest will be resolved after you meet the stowaways.