This solution is for post game play, for those who want to get it done the quickest way, rather than trying to do the story based missions. The missions required, do not have to be story-based missions, so the post game is actually a good place for this.
The easiest way I found to complete this challenge, after having beat the main game, was to simply do easy " power struggle " missions with a couple of dominated Uruk Captains.
First, round up 2 or 3 random Captains, and take the extra time to get at least a couple dominated. Having them dominated is important for the main purpose that their followers will not turn on you, and also it makes for easy one sided power struggle missions you can quickly complete, and simply keep fast travelling around the map. These missions are represented by the blue crest struggles around the map, and each time you complete one, simply fast travel to a tower, and a new mission should appear with the same dominated Uruk. Just make sure to not accidently kill off the dominated Uruk, and this will simply turn into a very precise grind to 30.
I found the Execution, and Trial by Ordeal missions the easiest of the missions, but all are easy to complete.
EDIT: Thanks to Chris Scarce, and MysticWierdo for mentioning the method about using the " Beck and Call " mission with a dominated Warchief, so that may be a way to do them fast also. My post-game, I did not have any Warchief's branded, so I simply used the easier Captains, and I did not think of trying the B&C method mentioned by them.
Also, if you simply enjoy just playing the game, and not worried about getting it done fast, the free DLC with Lithariel's quest would help to knock out a lot of missions, since that scenario is based on killing off all the Captains and Warchiefs without dying. Using the Power Struggle missions makes it easier to kill off some of them.