House Flipper 2

After progressing the "story" (doing email jobs) you will unlock the "Assembly" tab in the menu.

Open the menu with and over to Assembly, from there you can assemble a piece of furniture and get stars rewarded for how well you do.

Keep progressing the story to unlock more, and do all of the ones provided to you to unlock the achievement.
I'm unsure if doing assemblies themselves unlocks more, as I just checked after every story mission.

You don't need maximum stars for the achievement to unlock, as long as you get one star on each piece of furniture, it will still pop.

There are 12 Assemblies you need to do. 5 in the Simple section and 7 in the Moderate section. I have the achievement without the TV cabinet Complex assembly.

A simple guide listing all the available assemblies at this time.

Keep in mind 1 star counts and that's all you need. 2 and 3 stars give you a larger discount in the in game store. The discounts aren't needed as you will easily make more that enough money than you will need to 100% the game just by following the story and flipping a few houses. You just need to complete each assembly to get 1 star.

There are 5 Simple, 8 Moderate, and 3 Complex Assemblies. That may change later with updates or new DLC.

Simple Assemblies:
Picture frame
Table lamp
Clock
Shelf
Table

Moderate Assemblies:
Hanging cabinet
Cabinet
Desk
Bathtub
Nightstand
Radiator
Shower
Wardrobe Extension

Complex Assemblies:
TV cabinet
Wardrobe
Dresser

I believe at this time there no need in doing the Complex assemblies. The Simple and Moderate assemblies should unlock the achievement, but that could change at some point.

My achievement tracker stopped tracking at 83%, but it was showing 7-8% progress with each assembly I completed until it stopped tracking altogether at 83%.