This solution requires that you have advanced to the second map.
In the South of the second map, slightly South-south-east of the tower, there is a small cave. Before you enter this cave there are several plants on the ravines that lead to the cave. In the cave itself there are quite a few mushrooms. Using the route I have travelled in the video below you can gather 14 herbs in about three minutes. This will net you the challenge in about 25 minutes as you will need to repeat the process seven times and pick up a couple more herbs.
You can shorten the process by using Shadow Strike if you have acquired this ability to travel from the tower to an Uruk closer to the cave but their placement is quite random. While there are similar locations on the first map, I found this one to be the quickest and most abundant in plants.