During the campaign you may come across a communist faction task 'Help the Homeless' which requires to have no shacks on the map. You don't need to have the task active, however, it gives a good overview of how much shacks are left.
At the start of the mission, do not build any houses, but get mines and farms to get a good economy. Buy a foreign office, a ministry, and a minister of foreign affairs. Use the edict 'USSR Development Aid' when you can, else use 'Praise the USSR' and wait for 'USSR Development Aid' to become available. After using the edict, build apartment blocks where shacks are and use the 'Free Housing' edict.
To locate shacks, go to the Almanac -> Lists -> Residents - Housing. On the last page you'll see all people that live in shacks. Press on one, then select 'House: Shack' and press . The game will show you the shack. Just build an apartment block over it and he/she will move in after a month.