Enter the hotel room and talk to the man. After a fairly lengthy conversation you will fight with him. Follow the prompts and make sure you kill him.
As you go to leave the room with Clementine, a walker comes in, but ignores you be cause of all the blood and guts you are covered in. Kill it, then cut it open and smear Clementine with its guts.
You get the achievement when you leave the hotel.