If you don't want to die to get this, you can get it through rental income but without buying a house. If you complete the quest to become the proprietor of the Darkwood Bordello the income from this counts towards the achievement.
The Bordello can be found off Darkwood Lake. To become proprietor you'll need to do the quest to get the deeds from Grope and then talk to Madame Minzche. You don't need to do anything more than this, as the money will start to come in from this point. You get 570 gold per day, up to a maximum of 1710 (three days worth). You could continue playing and return to the Bordello to collect the gold every three days, but to speed things up you can teleport from the Bordello to somewhere with a bed and sleep for three days. Then teleport back to the Bordello (Recall), collect your money then teleport back to the bed and sleep for another three days. You only need to do this six times to accumulate 10,000 gold.