Pretty simple. Just play 5 matches of Extermination. Make sure you click "Public Match>Extermination" because if you click "Quick Match" it may place you in a Creatures vs Soldiers match which will not count towards this. An Extermination match consists of 2 rounds. One round you will be the creatures and you must prevent the soldiers from activating the beacon. The other round you will be the soldiers you must eradicate the creatures by activating the beacon to eradicate them.
You do not have to win these 5 just play 5 complete matches. You can join in the middle of a match and play to the end and it will still count.