Pure Essence is an essence crafted using the Essence Refiner. It uses a High Essence Core (top), Base Essence Core (bottom), Ender Essence (left), and Life Essence (right), with a Diamond in the center. These positions of the materials are required.
You will have to wait for a while, as the refiner takes its time turning your materials into Pure Essence. (note that the Essence Refiner requires power from an obelisk to transmute the materials into Pure Essence)
Pure Essence is not dropped from any of the guardians, like the ordinary elemental essences are; it must be crafted this way.