Very straight forward Achievement.
Once you load up the game after downloading the DLC. You will get a notification saying that there's a radio broadcast coming from somewhere in the north. Go to Northen Passage, enter, speak to the old guy and he'll tell you that there's a "weight limit" of 100. Just offload the stuff you don't need in a box to the side of him, you can retrieve your stuff once you finish in Zion. And once you have under 100 in weight. Just tell him you're ready to go and BOOM! 20 gamerscore!