Before We Leave

There are currently 4 scenarios in this game. You can not get this achievement in the 'Apocalypse Soon" scenario as stated in the achievement description. I got this playing "Hut-Owners Association". I would not recommend you try this in "Getting Busy" as you want to control and limit population numbers as much as possible, but then there is the advantage that you are confined to one planet and thus need to do less searching for islands that can grow cotton and have the sheep resource. Up to you if you want to try while completing that one, but my guide is more suited for the "Hut-Owners" or "Seed Hunter" scenario.

ETA: Even though the achievement description implies this can be done in the Seed Hunter scenario, it may not be possible. Sheep must spawn for this achievement. The likelihood that sheep spawn in that scenario may be very low or not at all. I would suggest not starting a playthrough on that scenario if you are only going for this achievement. It might be a waste of time. I replayed that scenario, and the Farming research remained blocked out and I never discovered any sheep or cows.

Key research needed: Clothing, Farming, and Spaceflight.

Clothing unlocks cotton and the manufacturing buildings needed, the weaver and tailor. You need to unlock Farming and then find a planet with the sheep resource in order to produce wool. You need wool in order to upgrade the weaver to produce good fabric which is then needed to upgrade the tailor to produce good clothing. A tip for finding an island that has sheep without having to colonize every island on a planet: look for sheep running around free on the island. You can find cows this way as well.

I would suggest when you colonize a new planet, do not immediately build a space port. I waited till I found the island with the sheep, and then built the space port to cut down on extra shipping. Though I suppose it doesn't matter much as you are going to have to stockpile good clothing by not allowing peeps to wear any clothing until we have provided enough for every peep in your game.

When peeps wear clothing, it degrades over time. It goes from good clothing indicated by the set of clothes with the up arrow to just clothing (minus the arrow) to rags pictured as a single shirt. So you can't just provide some peeps with good clothing and then the remaining peeps on the next boat trip for example. The first peeps will now be on a different rotation as their clothing will already be deteriorating while these others have new good clothing.

In order to get every peep in your game clothed with good clothing at the same time, you need to know how to prevent them from using this resource until you are ready. To do this, you press Right Bumper while over a populated island. Now go over to the 4th box on the top row with the clothing icon. Click that, then go to the 2nd row, 2nd box. Here you can reserve clothing for "transport and construction". Go down to the second bar and move the slider to the right to the number of peeps on this island (or more if you have a warehouse storing excess for transport elsewhere.) This will stop them from going to the tailor, warehouse, or port and taking clothing.

You must do this for every island on every planet that has peeps.

I consolidated peeps on as few islands/planets as possible by using trade ships and trade space ships to move peeps around. You don't need to, but this just means your trade/warehouse network will be larger.

Once you have enough good clothing stored at the port, space port, and/or warehouse, on each island populated with peeps, PAUSE THE GAME. Leave the game paused while you go to every island and now move the slider back to zero for the amount of good clothing reserved for transport and construction. Unpause the game and give it about a minute or less on the fastest setting for all the peeps to aquire clothing from wherever you have it stored. The achievement should pop when this happens.