Essences can be corrupted by using a Remnant of Corruption on a monster trapped by Essence before releasing it. Monster may gain one additional Essence.
With your remnants in your inventory, you want to find a monster trapped in an essence crystal that already has four essences attached to it. Then you want to use one of your remnants (by pressing Y) to corrupt the trapped monster. If you are lucky this will add a fifth essence mod. Releasing and then killing the monster will grant you the challenge. If you are unlucky will need to search for another monster trapped with four essences to use another remnant of corruption.
There is no guaranteed way to find a trapped monster with four essences.
Buy PoE Currency Cheap