Carved of the Undermine

This is attained by earning item level 645 in each slot.

This achievement watches hidden "highwater marks" that record your highest looted items, not actually requiring you to equip them. Most slots are obvious, but your rings, trinkets, and weapon slots have special hidden requirements. Code-wise, you can either query C_ItemUpgrade.GetHighWatermarkForSlot(x) where x is a number from the Enum.ItemRedundancySlot table, or you can check hidden currency ids from 2264 to 2280.

Rings and trinkets wait until you have two items you can equip at the same time before being counted, and you can't swap spots like past achievements. This means you can't just loot the same ring/trinket again since most of them are unique-equipped. The ring/trinket tracker basically looks at your second highest piece. However, there's a bug as of this comment (it may have been fixed, it worked in Season 1 and I tested the first week of season 2) where deleting your Cyrce ring and getting another one from [npc=230242] will mark rings complete for Weathered, Carved, and Runed achievements (item level 658).

Weapon slots are a little more complicated. There are five trackers in three groups: "Twohand" by itself, "MainhandWeapon" and "Offhand" for non-dual-wield, then "OnehandWeapon" and "OnehandWeaponSecond" for dual-wield. The achievement marks your weapons complete if any of these three groups meet the item level criteria. For some examples, a strict Twohand spec like Retribution or Blood needs to loot a high Twohand and the achievement ignores the other four trackers. If you're a Mage, Priest, or Warlock, you can loot a high staff to mark Twohand complete but you can also get a high onehander and a high offhand to mark "MainhandWeapon" and "Offhand" complete. Dual-wielding specs like Rogue will mark "OnehandWeapon" and "OnehandWeaponSecond" complete. Shaman gets the option to mark any of the groups complete depending on what spec you're in, like if you receive a high twohander while Enhancement, switching to Elemental should mark weapons complete.

I made the following chat script that will not show the other weapon trackers if any of the three "groups" I explained above have met the item level criteria:
/run x={}for n,i in next,Enum.ItemRedundancySlot do w=C_ItemUpgrade.GetHighWatermarkForSlot(i)x={w>644,w,n}end for i,v in next,x do if i<12 and not v[1]or i>11 and not(x[12][1]or x[13][1]and x[16][1]or x[14][1]and x[15][1])then print(v[2],v[3])end end

Got everything to 645 and still not working?
1) Log out and back in (this is what did it for me)
2) Remove all items and wear them again.
3) Try logging out and back in again.