Abominable Lives

I took Varenne table and I updated it to match with the knowledge we have by now, in patch 9.1.5.

If you want to do this achievement and the whole Necrolord specific feature the fastest and the most optimized way, you should think about the number of quests each construct gives (random every week) and their price in Superior Parts (timegated resource). That is why I would suggest this construction order : Chordy > Atticus > Marz = Mama Tomalin > Roseboil > Professor > Sabrina > Flytrap > Toothpick > Gas Bag > Guillotine > Iron Phillip = Naxx

I personally preferred to construct Professor and Sabrina before Flytrap, because Flytrap gives the same quest every week, so there isn't a random if you will get or not his quest for the achievement. However, you should count how many superior parts you can get every week at each moment, also counting how many you can get the next week (considering the superior parts which is refunded to you for making the quest of the construct you just made) and making another construct than in this order would be more profitable at the end of the day.

Constructs

Abominable Lives

Construct Body: "Chordy"

Shinies of Bastion
Things They Leave Behind
A Bountiful Haul
Something Old, Something Used

Construct Body: "Atticus"

Asset Extraction
Supply Chain
A Brokered Deal

Construct Body: "Marz"

Field Training
Arboreal Tactics
Training Program

Construct Body: "Mama Tomalin"

Baker's Dozen
Give A Dog A Bone
Pie Not?

Construct Body: "Roseboil"

Cure For All Ills
In A Bad Light

Construct Body: "Flytrap"

Corpse Run

Construct Body: "Professor"

The Two Sides of History
Scrounging for Scrolls
One Lich's Trash...

Construct Body: "Sabrina"

Fighting Words
The Last Word
Say The Magic Words

Construct Body: "Toothpick"

Old Stomping Grounds
Digging Around

Construct Body: "Gas Bag"

Herbicidal Tendencies
Special Formula

Construct Body: "Guillotine"

Grinder
Hands on Approach
Cut 'Em Down to Size

Construct Body: "Iron Phillip"

Bring Your Own

Construct Body: "Naxx"

Drink to the Dead

I hope this comment and my suggestion will help you !
Happy stitching !

The last four quests I need haven't shown up for a month. You can finish Pursuing Loyalty in one afternoon, Be Our Guest in 5 resets, Mush Appreciated in about a month, but Things To Do When You're Dead needs unknown amount of resets. If you're lucky enough, it could be few weeks, if not, it could be months. Whoever designed this should be sent to Torghast immediately.

Can't wait to be given the RNG middle finger for the next 9 weeks and not get the veilstrider title.
Need 1 quest each from 8 constructs and learning they're random just hit me in the gut hard.
Can't imagine how anyone else feel who is now working on this last achievement before 28th Nov.

Update 8th oct: Got 1 quest out of 8 needed from 8 different constructs, pray harder guys!
Update 12th oct: Got 6 out of the 7 last quests, now just need "Shinies of Bastion" from Chordy.
Update 19th oct: Quests seem to be regionwide and this week Shinies of Bastion is up and my journey is finished.
Good luck to anyone else trying to reach the finish line.