To get the 20k you have to go through every mission in the dark brotherhood. It will take a while but it shouldn't be too difficult. In the final quest you are paid 20000 septims for an assassination, when you return to the dark brotherhood Nazir will ask how much money Amaund left in the dropbox. What ever amount you tell him he will send you to have the sanctuary refurbished. Now the quest is finished you get the achievement, and its completely optional for you to spend your money on the Dark Brotherhood. Also you will get a quest called The Dark Brotherhood Forever, you can keep returning to the Dark Brotherhood to receive new contracts, upon the completion of each contract you will receive anywhere from 600-1200 septims making this an easy flow of money.
Happy Killings!