Multitool
One of the settlers must equip at least 3 tools
If you're not going to micromanage (like me), you will likely get this achievement by accident. Settlers get their tools by themselves, as they need them. If you don't assign them exclusively to a task, they will take the required tool from the stockpile. It's a good idea to always have 1-2 of each tool in stock. It's always cool to have Jack-of-all-trades in your settlement.

First ceramic
Fire your first ceramic pot
You likely won't get far without ceramic pots. You will need to mine the clay deposits on the map, create Unfired pots in the Crafter, then turn them into Ceramic pots in the Kiln. Ceramic pots are useful for cooking and research. I guess those clumsy settlers kept breaking them, because I always needed more, even when they weren't used for research.

Tribe
Have 15 people or more in the settlement
The settlers are pretty chill when it comes to lodging and threads, but it's a good idea to be ready with 3 empty house slots for resting (there are houses for 1 to 4 settlers) and optionally with regular clothes (for protection), warm clothes for winter (or they will retire to their homes more often AND NOT WORK!) and tools (so they can get to work faster). You're not going to let them starve in the cold in their bare a$$es, are you?

First bread
Bake your first flatbread
This one is pretty optional if you focus on other foods. The settlers don't get any benefits from eating a variety of foods. Still, making the recipe isn't very difficult and seems to be a bit more efficient than Pea soup. You need to harvest Barley, break down the Sheaf of barley into Barley seeds (with the byproduct Hey) in a Thresher or Thresher floor, and bake the bread in the Clay oven.

First copper
Smelt your first copper
Producing copper requires Copper ore from deposits on the map (you have to look for it). Grind it using a Mortar and pestle (or the faster Mechanical crusher), and smelt it into Copper at the Bloomery. You will also need a Charcoal Kiln for the Coal. Make sure to build a Mine on the Copper mountain to spawn new deposits. As a side note, Copper becomes obsolete when you get to Bronze, then that too is inferior compared to Iron.

Best Friends Forever
Send a settler with a dog to hunt
Domesticating Wolfs turns them into faithful Dogs. Magic! This is the way I got this achievement: when I saw the settler head out to hunt, I selected him, clicked on Assign a pet and chose a dog. Let's not mention that the poor guy was hunting a Mammoth and the dog... didn't make it. But the settlers got a good meal out of it. I don't remember if the dog's meat was also recovered, but the settlers definitely eat anything that moves.

Village
Have 30 people or more in the settlement
This should happen after you accept the settlers that are offered regularly. They come in sets of 1 to 3, with some items on them. More often than not, naked, even in the winter.

Denied
Refuse to accept a nomad into the settlement
Since it seems pretty rare that new settlers come to your settlement, it's best to wait for when the game offers a single settler. You will thank yourself for the City achievement.

I survived 100 days
Survive 100 days with at least one settler
Not much to it. Just make sure to have food, shelter and clothing for nice, productive settlers. It's difficult to keep track of which Defni (one of the too-few settler names) is the oldest one, so try to keep most of them alive. It might not matter to have a settler from day 1, just to reach day 100.

First bronze
Smelt your first bronze
Similar to First copper, but has a different recipe. Check the Bloomery.

Are you sure it doesn't stink?
Cook food using dried manure as fuel
Manure comes from domesticated animals in the Animal pen. You need a Manure drying area which, as the name might be unclear, is an area in which manure is dried. Cooking with manure didn't get any complaints from the settlers. These guys will eat uncooked meat off the floor.

First iron
Forge your first iron
Similar to First copper, but has a different recipe. Check the Bloomery.

Back to the future
Start the time machine and go back to the future
Researching the Time machine takes 14k research points and then 100 Iron to build. It's less intimidating than you might think, primarily because you have Iron available. Expand your Iron production line if the process is too slow.

Engine of progress
Research all technologies
Takes a bit of time, but is made much more efficient after you use Iron in research.

City
Have 60 people or more in the settlement
Just like the Village, but takes more time. This was the last achievement I got. By that time I had stable food production with 10 Clay ovens, so all I did was regulate Wood chopping to fuel the 10 Charcoal kilns (Coal is more efficient than Wood) to create fuel for the ovens, while running the game at full speed. Obviously, I got to 58 settlers, hoping to get the achievement with one more batch. The game gave me a set of 1, so I had to wait for another batch. Of course, the last batch was with 3 settlers, as if I needed more mouths to feed. Lazy bums...

Homemade production
Sell ​​10 units of bread, cheese, woolen fabric, a pot of wine, and honeycombs at a trading post at the same time
The achievement wants you to sell these items in a single trade deal, but the wording in the achievement may be unclear:
- 10 Flatbread
- 10 Cheese
- 10 Wool cloth
- 10 Pot of wine
- 10 Honeycomb
Promise me you'll save before the deal, trigger the achievement and then revert to the save. No use in wasting resources, right?