These fetch quests are given to you by random NPC's dotted throughout Middle Earth. They are marked on the map with a ? symbol. They ask you to find an item that they have lost or was stolen etc.
I had alot of trouble with what to do for this achievement and was unable to google a solution because after getting a quest you will see a trail of ghost studs that lead to nowhere and nothing.
The items they require are actually obtained from the story missions and the story they tell you about them item points to the mission in which you can find it.
I recommend completing all the story missions first so you have all the items before you talk to the quest givers.
Another tip is to get the red brick called Quest Finder which will give you white arrows pointing to the quest givers in the overworld.
Not technically a solution but some useful info as this one had me scratching my head for a while and there was no guide here, so i hope this helps.