Corrupted Zones are areas with "Corrupted" machines that are Red on your Focus, are higher level than normal, have more health, leave a red "corruption" trail that hurts you if you touch it, and cannot be over-ridden. Corrupted Zones are denoted by a white circle with a cross-hairs in it on the map and contains a number of corrupted machines.
There are 11 Corrupted Zones on the map, and 2 have to be cleared (doesn't matter which 2) to progress the story and open the map beyond the first area. (however you can escape the first area to the far north without going through Dawn Gate, where you are required to clear 2 corrupted zoned before they will let you through)
When you Discover a corrupted zone in the world a quest will open to clear the zone. Check your quest log or click on the map location to see the level of the zone. Once cleared the map location disappears.
Before you enter a corrupted zone make sure you are stocked up on health and fire-based ammunition as corrupted enemies are naturally weak to fire regardless of base machine. For higher level zones I personally recommend having the Double Shot or even Triple Shot skill to get creatures burning faster.
Set a few traps if able and then prepare to fight. Keep an eye on the neighboring areas as normal local machines can be aggro'ed into your fight.
Once you've cleared all 11 Corrupted Zones the trophy will pop.