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.