Master Relic Hunter

Harrison Jones appears in some people's garrisons each day, offering a random quest (which random quest is the same for everyone region-wide).

Here are the various quests you'll want to look for, for each part of the achievement:
The Blessing of Beasts - Treasure Contract: The Thunderlord Sage
Breaching the Barrier - Treasure Contract: Explosive Discoveries
The Apexis Device - Treasure Contract: Amulet of Rukhmar
The Spirit Forge - Treasure Contract: Gutrek's Cleaver
Taking from the Taker - Treasure Contract: The Infected Orc
The Crystal Reborn - Treasure Contract: The Artificer

Didn't get Harrison in your garrison? Check out group finder! There are typically people sharing their garrison perks, including the daily NPCs. Don't worry, you can turn in the chain when you're done back to SI:7 in your own garrison.

Completing this achievement awards you your own Harrison Jones as a follower. After that, instead of Harrison, you'll get Surveyor Daltry standing in as the daily quest-giver.

[

Start the quest in [npc=89793]

Criteria

Treasure Contract: Amulet of Rukhmar

The Apexis Device

Treasure Contract: The Artificer

The Crystal Reborn

Treasure Contract: Gutrek's Cleaver

The Spirit Forge

Treasure Contract: Explosive Discoveries

Breaching the Barrier

Treasure Contract: The Infected Orc

Taking from the Taker

Treasure Contract: The Thunderlord Sage

The Blessing of Beasts

I was having trouble keeping track of my achievement progress on alts, as the achievement requirements are titled differently to the starting quests for each treasure hunter chain.

I wrote this macro to make things easier

Alliance

/run if(true)then local q={"The Thunderlord Sage","Explosive Discoveries","Amulet of Rukhmar","Gutrek's Cleaver","The Infected Orc","The Artificer"};for i= 1,6,1 do local a,b,c=GetAchievementCriteriaInfo(9825,i);print(q,": ",a," = ",c)end;end


Horde (Thanks to the correction from HughJarse, the achievement ids are different, aparently)

/run if(true)then local q={"The Artificer","Gutrek's Cleaver","The Infected Orc","Explosive Discoveries","The Thunderlord Sage","Amulet of Rukhmar"};for i= 1,6,1 do local a,b,c=GetAchievementCriteriaInfo(9836,i);print(q,": ",a," = ",c)end;end


It will give 6 lines of output (one for each criteria) containing the starting quest name, the matching achievement criteria, and whether it has been completed or not.

eg.

The Thunderlord Sage : The Blessing of Beasts = false

edit: Updated macro to contain the variables declared within the macro, i.e. it doesn't pollute the global variable list.
edit 2: Had the "Infected Orc" and "The Artificer" the wrong way round.
edit 3: Added a Horde version of the script. (not tested by me). The achievement ids are different apparently. Thanks to HughJarse for the info.
edit 4: Corrected the quest ordering for the Horde Achievement, thanks to Nytespawn for the update