Jeepers Creepers
Stumble into a spider cavern in the underground

A spider nest is a mini biome that is found underground, most notably the cavern layer. The inside of the nest has a black background and is filled with cobwebs. Once found on your map a spider nest will have a black and white checkered pattern. It is said they are more likely to be found in the tundra or forest biomes and also they can be found close to mushroom biomes. I found a couple of nests on the border of the tundra and forest biomes just above where you see lava. Once you are deep enough in the cavern layer, I suggest using a Dangersense Potion. If you dont have the potion already, to craft this potion you will need: 1 Bottled Water, 1 Shiverthorn, and 10 Cobweb. When consumed this potion will make cobweb areas sparkle red. Once you find a big red sparkling area, you will know you have found a spider nest. Dig inside and you will get the achievement. I will post a screenshot of how deep I was to find a spider nest and also of what the nest looks like using the dangersense potion. I hope this guide helps you and best of luck.