An easy time to complete this is while doing the optional One Ring mission "Strength in Numbers." Just build up your combat multiplier and use the Flash Brand skill (
+
) to brand part of the enemies around you, and you should have it in no time.
Also, if you're having trouble, using the wraith flash will eventually fill the one ring's power and you could use that to have unlimited Flash Brand for a short time.
Edit: Some people have commented that they found this to be easier while doing Test of the Ring. Additionally, if you have any trouble with the achievement popping, try removing any epic runes.