I struggled too....
...then i did all the first 7 campains on normal difficulty. I did all 7 stages on all these campains and earned an Item in every battle. When i got a shard or a toon...i did the stage again until an item dropped. After i completed all the battles the weekly mission was finished
good luck, hope it helped
I finished mine recently, I was farming stars in brutal and it somehow the artifacts for the basic sets were complete for me after i finish .
So overall u can try Brutal maybe farming but make sure to get all the artifacts from all basic sets required . Try Kaerok Castle first and test if it start counting for u when u complete the whole set for Life artifacts. :)
It has to be TWO different types of artifacts from each set. 3 boots counts as only one. It has to be like one boot and one shield.Seems to be more than two artifacts from each set required. I've just gotten three boots from each set out of the campaign and still says 7/14.
Edit: When I went back into campaign and got a weapon from each set it was completed so I guess it requires 2 different types of each set.