UPDATED! Due to this game exiting preview and the 1.0 release, the previous guide was no longer valid.
Currently, the eaiest Tier 3 item to craft is the Termite Axe. To get the recipe, you need to kill a termite and analyze either the termite chompers, termite parts or tough gunk (previously called "bug gloop"). Then collect enough materials to craft, (2 termite chompers, 2 crow feather pieces, 4 tough gunk) and craft the item at a workbench. Due to the relative ease of termite soldiers compared to other Tier 3 enemies, and ease of obtaining enough materials, this is the simplest Tier 3 item.
Termites can be found in and around the wood pile in the north-west part of the yard, west of the shed. Termite workers will provide tough gunk. You will need to kill 2 termite soldiers for their chompers, so you will probably have to venture into the termite nest to find them. Crow feathers can be found across the backyard, but notably under the mysterious machine lasers, and under the birdbath.
The other options to get tier 3 recipes are, in my opinion, more challenging overall. These include killing the Broodmother, killing a black ox beetle, finding the spicy coaltana, or unlocking the sunken treasure chest in the sand castle moat, amongst others.