In episode 4 after discovering your name (by talking to Hurley) and gaining access to Swan Station you will be locked inside.
Wait until you get locked in and the beeping starts and a door near where you start opens.
Enter the room and use the computer in the middle of the room, entering "4 8 15 16 23 42" (don't forget the spaces) and finish with the "execute" key.
The achievement is yours
I messed this up because none of the guides mention to use spaces and i didn't assume i had to