What the achievement asks
Serve tea to eight named characters during the Venthyr assault on the Tremaculum. Five points, account-wide.
The assault has to be offering its tea quest, and then you have to find eight specific people among the fifteen you serve.
You cannot see them until you are Tubbins
Talk to Tubbins and you become him, and only then do the named characters exist as far as your screen is concerned. People walk the whole Tremaculum wondering where everyone is.
You can step out and talk to him again to get back in.
The eight
They are not all present at once. Four tend to be up on the first day of the assault and four on the second, so plan on two visits.
The mistake that ends the attempt
Do not finish the quest's own objective before you have served all eight.
Serving fifteen allies completes that part of the quest, and once you then leave vehicle mode you can no longer interact with the Dredger to serve anyone else, even with the quest still sitting unturned in your log. The cycle is over for you.
Count carefully, and serve the named characters first. If it happens anyway, abandon the quest and take it again.
A small kindness for alts
Iven takes tea repeatedly without picking up the debuff the others get, so if you are running this on another character and only need the quest done, all fifteen servings can go to him in a few seconds.
Where it fits
One of the nine under On the Offensive, which now needs only four of them. It is a good fourth pick if the tea quest happens to be up while you are collecting the three that do not depend on luck.