The Wandering Village

I recommend doing these in 3 separate playthroughs as it can get quite difficulty.

Master Gatherer

Survive until day 100 without building any Farms
Can still build a mycologist and a herbalist. Multiple of the berry gatherers are your best friend here to get a lot of food and new spawns happen often.

Strict Diet

Survive until day 100 while using the Onbu Feeding Trebuchet a maximum of 3 times
Recommend doing this in the same playthrough as the above achievement as these 2 are the easiest in my opinion. The best way to get this, is to first get the main research needed for running through deserts then focusing on getting the food liquefier and feeding pump since this does not go towards the achievement. Will only need to use the food trebuchet once, maybe twice while waiting for the research and building.

Dry Spell

Survive until day 100 without building any Air Wells
This is actually a little harder than you might first think. This basically limits to only getting water from the desert biome. Make sure to use plenty of cactus farms and send scavengers to the oasis whenever possible. Use water tanks to stockpile as much as you can and once again use berries for food. You will need the water for herbs and mushrooms so try not to use it on other farms that will require water.

Agricultural Revolution

Survive until day 100 without harvesting any Berries
Honestly this achievement is a bit annoying, I have done multiple playthroughs so I can confirm that this means even clicking the sickle to get rid of the berry bush will not work. Placing buildings on top of the bushes also will just harvest the bush before the building is placed so that does not work either. This also includes farms when adding plots, make sure not to overlap it with any position the berry bush is in.

Only way I can suggest doing this is having a setup in mind really early game and using a cheap building, such as a hut, as a placeholder so that berries do not grow in those locations. Build most of your buildings in the dirt sections and only place the farms and herbalist on the grass since they are the only buildings that need to be in those spots.

Playing on the tutorial difficulty, this is a fairly easy achievement, albeit a tedious one. You'll be introduced to the trebuchet structure early on in the game which you can use to feed Onbu. You must not do this more than 3 times before day 100.

There are two ways for Onbu to get nourishment which do not void the achievement:

1) By coming across natural food formations that Onbu will stop and eat from. These appear as clusters of mushrooms on the regional map. This will typically fill the beast up to zero hunger. Just make sure you don't order Onbu to walk through the food spot without stopping.

2) By constructing a feeding pump and directly injecting Onbu with food. This is a far less reliable method for the first 100 days as the research for this is far down into the tech tree and will take a lot of time and knowledge to complete.

Personally, I'd stick with method 1). You can keep an eye out for mushroom patches from the regional map. I found the most spawning in the jungle and ocean environments. By the end of day 100, I only used the trebuchet twice, including for the tutorial.