The Elder Scrolls V: Skyrim Special Edition

Update: Just a warning from @Karnivore12

For anyone still trying to get this, be safe and don't do the quest Boethiah's Calling before getting the land for Falkreath. It will glitch the Kill Raider Leader quest at Knifepoint Ridge and you won't be able to buy the land. Also, don't progress through the Dark Brotherhood quests, as there is a quest that will reduce your favor to the Jarl of Falkreath. Basically, don't be like me and have to create a third save game to be able to unlock this achievement.

Solution:

1. Become thane for falkreath, dawnstar and morthal (NOT REQUIRED, I initially thought it did but it is not, READ UPDATE BELOW) I'll leave this just for anyone interested in being thane but if you dont really care just read Heraizen's comment and proceed to step 2

To become thane you have to go the jarls of each area and they will give you a quest. After doing the quest you then have to speak to the jarl again to get another quest which you have to help 3 residents of the 3 respective areas.

Morthal
Sell iron ore to Gestur
Sell firewood to Jorgen
Fist fight Benor

Falkreath
Sell firewood to Hert (she is not in falkreath but somewhere northwest from it, near the lake)
Retrieve berit's ashes to Runil
Sell potato to Mathies

Dawnstar
Give karl an alcoholic drink
Sell quicksilver ore to Leigelfe
Sell iron ore to Beithild

Above is the list of easy ways to help them.

2. After becoming thane on each area you can buy a pot of land (5000 gold) for 3 different areas go the areas and you have to build the houses. They will provide you with some materials in the chest but you will still need a lot of sawn logs(bought in lumber mills or you can get them by cutting lumber, note : not chopping wood ), iron ingot, corundom ingot and quarried stone.

3. Build the houses with the materials and you HAVE TO BUILD THE THREE WING EXTENSIONS OF EACH HOUSE and on the last house you are trying to build, MAKE SURE TO MAKE AN EXTRA SAVE BEFORE BUILDING IT because i had an issue where it didn't pop so i reloaded my autosave and i got it by doing the same thing.

Good luck and welcome back to Skyrim.


Update : Credits to OSSISS, Heraizen and Kennyannydenny for confirming, you don't have to be thane.

according to Heraizen :

For those confused why you can't buy land, often the option will be to buy a house, after selecting this option they will tell you that there is no house available and then offer you land.

Also I can confirm you do not need to be Thane.

Dawnstar - Complete the quest "Waking Nightmare" and then a radiant "Kill the Giant" quest for the Jarl of Dawnstar.

Falkreath - The quest from Jarl Siddgeir to bring him a bottle of Black-Briar Mead and then another radiant quest to kill a Bandit Leader.

Morthal - Complete the quest "Laid to Rest" for the Jarl of Morthal (who is different depending on which faction you sided with in the Civil War quest-line).