If you don't want to do 4 dungeons each week in order to get the Mastery of the Turbulent Timeways achievement and mount, you only need to run 1 a week.
The Master of the Turbulent Timeways required players to get the Mastery of Timeways buff every week for 5 weeks. To get Mastery of Timeways, you need to do a total of 4 dungeons to stack the buff up to 4 before it expires.
However, if you get the Mastery of Timeways buff and roll it over to next week, you only need to complete 1 dungeon the next week in order to get progress for the achievement.
As Mastery of Timeways doesn't tick down while offline, you may wish to get the buff on a character you don't play much so that you only need to do one dungeon each week!
When you complete all 5 weeks, you get the Sandy Shalewing Mount!