Hap'he

During heavily-restricted PTR testing the only thing affecting the Finally At Rest progress was the The Big Dig: Traitor's Rest Weekly. One turn-in added 17%. When there's no other source, this will result in at least 6 weeks to complete the achievement and get [item=213134].

Update January 17th: Right now the progress seems to be bugged because it's no longer character-specific (obviously not intended, because progress is tied to new entries in Eadweards journal and we only see them once a week). This means, right now, you can shorten this down to ~6 hours (and even less for characters played simultaneously) by completing the The Big Dig: Traitor's Rest Weekly on six different characters.