For anyone having troubles with the achievement I found this in the Support page of Bethesda:
What are the specific requirements for getting land in each hold?
For Falkreath: You must complete the “Rare Gifts” favor, and the “Kill the Bandit Leader” favor. You may then buy land from Steward Nenya.
For Hjaalmarch(Morthal): You must complete the quest “Laid to Rest”. You may then buy land from Steward Aslfur.
For Dawnstar: You must must complete the Daedric Quest “Waking Nightmare” and then the favor “Kill the Giant”. Please note that this favor has the prerequisites of being level 22 or higher, and having had previously completed the “Waking Nightmare”
Now the recomendation For Falkreath:
Even if the player has become the Thane, Siddgeir may continue to greet them by saying, "Something you need, you miserable wretch?" This is the result of a negative disposition towards the player, possibly caused by completing the Dark Brotherhood contract on his Housecarl Helvard. Doing quests for the Jarl to become Thane after completing that contract seems to counter this and raises Siddgeir's disposition towards the player.
In Morthar there's no problem around, just avoid to be a bad dovakhin and don´t kill the steward of the Jarl.
And For Dawnstar:
The Waking Nightmare begans talking with Erandur in The Windpeak Inn in Dawnstar after that you go through the mission then the Jarls ask you a favor (Kill a Giant, BTW, You can also get from somewhere the same mission, to kill the same Giant, so if you go to kill it after the Jarls asked you to do it, you'll complete 2 missions for the price of one).
If you don't recognize Erandur, He stands around in The Windpeak Inn in Dawnstar. (when he's not sleeping)