Pretty simple to get quickly, but you will need at least 19,500 caps, if you haven't already upgraded any rooms to level 3 and don't have more than 1 living quarters.
Simply create some living quarters (to ensure this is as cheap as possible, don't build it next to an already existing one), press
and select to upgrade for 250. Then upgrade again for another 750. Destroy the room, build another, upgrade twice, then rinse and repeat until the achievement pops.
N.B as with all achievements in Shelter, progress is
not cumulative across vaults, so this must be done in a single vault.