Master Carpenter is about completing making items at the carpenter buildings in your world. For Master Carpenter 3, you will be required to make 1000 items using the carpenter buildings to get the gold medal in-game and unlock this achievement. The 120 items you made to get the bronze and silver medals in-game will count towards this achievement. The carpenter can make stools, chairs or wheels - all count towards this achievement. Making stools will require nails and wooden plank resources to be available in your warehouse. Making chairs will require cloth and wooden planks to be available in your warehouse, Wheels require...
Levelling the carpenter building will allow access to making Chairs and Wheels and increase the rate of productions. Using a carpentry specialized resident and levelling that resident to work in the carpenter building will also increase the speed at which items are produced.