Work towards getting this achievement when grinding the ten victories with 2-player games. Send both of your players to college and hope one of them gets the Doctor career. If neither does, you can just restart the game. Play through the game all the way, making sure not to lose your job or switch careers with your Doctor. Then, when the option comes to buy your second house, purchase the Mansion. It costs $800,000, but you can take out a loan to get it if need be. The achievement will unlock right away.
NOTE: Only one player can buy the mansion per game.