This will come naturally while you progress through the game. Simply pick up all orange items that are dropped.
I was doing patrols for a long time and got them mainly from defeated super-villains but you will get some storyrelated ones as well and I think they can also drop from loot boxes and other enemies.
From what I experienced you only have to loot them but you can sell or destroy them once the where in your inventory. It will still count towards the achievement.
Also you don't have to collect em with one hero. For me it popped when I was running with my 2nd char so picking up any artifact with any hero will raise the counter.
Further I don't think that you have to collect 100 of the same artifact but need confirmation for that. Hope this helps a bit. Happy looting.