When you start the game this achievement should be your main concern. You will get most of the others trying for it. It is mostly luck based but without a strategy you'll miss your opportunity over and over and over again.
You will need both Dark Blue properties whether legit or with Wild Cards, a House, a Hotel, the Double Rent and the Green/Blue Rent cards. Multi colored Rent cards do NOT qualify.
Play a local match against just one Easy AI. Getting the Dark Blue cards are the least of your worries. Keep restarting the match til you have at least 2 of the buildings or Rent cards.
Don't try to win. Prolong the match as best you can. In the beginning focus on having money in the bank and stifling the AI so Rent doesnt decimate your property cards. Don't put down a Blue property til you have a plan to put down both at once or the AI will steal it. It will take a minimum of 2 turns to get the kill move for the achievement probably three turns though unless all 6 cards are in your hand. Make sure you have enough moves left to add the Double Rent to the Green/Blue one or the opportunity is lost.
Keeping 6-7 cards in hand seems to work best, holding onto cards the AI needs to win. Discard the cards he needs instead of playing them so he can't steal them. Try not to allow enough cards for a set even onto the board.