So I have the most awesome neighbor. He's working very hard and so far got 3 badges not including the explorer badge. He doesn't know if there is a magic number (of actions), he's more inclined to think that badges are random drop like alicorn parts and shards.
Chef badge: cooking feasts in the kitchen. He made about 20 hearty feasts, 10 valentines, and probably 20 other feasts.
Nurturer: comes from watering stuff, mushroom, tree, fruit trees. He's watered hundreds of things and badge came while watering a crab apple tree
Slayer: about 200 beasts total, badge came upon slaying a fangbeasts.
I also have a neighbor that got the farmer badge after growing 66 strawberries. We all know it's quite random because we all grew a lot more crops than that and didn't get badge.
I think if badges are like shards or alicorn parts then there's no need sweating over this goal. Just carry on and badges will come someday. Good luck everyone