What the achievement asks
Put any Heart of Azeroth Essence of rank 4 into the neck. Ten points.
Not account-wide. The character with the neck is the character that earns it.
Rank 4 is the highest, and only some Essences reach it
Essences come at ranks 1 to 4, and rank 4 is the last. You need exactly one of them, of any kind, so the sensible approach is to find the single easiest rank 4 available to you rather than pushing whichever Essence you happen to like.
Sources vary enormously between Essences: some rank 4s come from reputation, some from raid bosses, some from rated play. The cheapest rank 4 you can reach is the right answer here, because the achievement does not care which one it is.
What has to be done first
- Have a Heart, the neck
- The Heart Forge, without which no Essence can be slotted at all
Its harder sibling
My Heart Container is Full wants rank 3 or better in every slot, which is a far larger job than one rank 4 in one slot.
The two do not conflict: a rank 4 counts as rank 3 or better, so the Essence you slot here is also one of the slots filled there. Anyone intending to do both should pick their rank 4 with the other achievement in mind rather than treating them separately.