To get this achievement you must go to Little Vegas nightclub in Downtown Colorado Springs. This will happen shortly after you finish up with the Garden of the Gods and get the quest "Big Trouble in Little Vegas". In the club, there are six named prostitutes upstairs in separate bedrooms. Pay them $10 each and you'll catch a different STD from each one. After this, find a pile of snowballs (there's one near the dogs outside the club) and pee on it. Gather some yellow snowballs and keep throwing them in the character with the diseases until you get Denver Rot, the last STD needed with a 5% chance to apply.
This is missable depending what ending you'll choose in "Big Trouble in Little Vegas" quest.