Cause He's The Ax Man To craft a stone Axe you need to open up your menu and go into the Crafting area. Once in the crafting area you want to use LT and RT to navigate the crafting area to the tools which is a screwdrive and wrench crossed, the stone axe will be under this category, you will need to collect (with your fists) 2 fiber, 2 wood, and 2 small stone (you can find on ground or just hit RT on a rock until you have 2).
Just hit
on the Stone Axe, then
on the D-pad and it will automatically craft, once done the achievement will be yours.