Shortly after speaking to agent Humphries at the police station you'll have to visit Lucy, she'll tell you she doesn't know where The Captain is, go and talk to Higgins, he's the young boy just across the road and he'll tell you that The Captain is just down the street.
After you find him you'll discover that he's ill, fast travel to the hospital and buy him some medicine, once you return to him and hand over the medicine the achievement will unlock!
If you find yourself stuck on a particular part of the game be sure to check out this excellent video walkthrough of the entire game, the users youtube channel can be found here;
http://bit.ly/ih2LIC. Alternatively I've linked in the first video below and you can use that to reach his channel.
* Credit to adventuregamefan for the video