Like the quest "Task: Kadara’s Ransom", this one relies on you finding randomly spawning quest objects (in this case Weapons Caches) in unmarked Outcast/Collective camps across Kadara. You know how this works by now, sack enemy camps as you find them, search for that magical magnifying glass that indicates such an item can be found (SAM’ll often call it out, as well), then scan the Weapons Cache. Once you’ve scanned three Weapons Caches you’ll get a navpoint, directing you to the southeastern edge of Kadara’s operational zone.
From the Forward Station near Kadara Slums drive east, then turn south at a fork and follow the road southeast, past another Forward Station further on. The navpoint you’re looking for leads to a camp just north of the road, just after the road turns east. This is also near Johan’s hideout in the quest "Out of the Frying Pan". Enter the abandoned camp and search some crates to find a Datapad "Shipping Notice", which discusses very, very bad intentions for Prodromos.
Well, this obviously cannot stand. Either get back in the Nomad and continue following the road east, then north to reach your destination, or simply head down a rocky slope to the northeast and make your way there on foot. When you approach your destination - a series of structures on a short bluff - you’ll find that this area is most decidedly not abandoned. Not only are there the typical Raiders and Sharpshooters stationed here, but more troops will be deployed via dropship as soon as you arrive. On top of that, you’ll be facing a new foe - the Hydra. This ponderous mech can, in addition to its standard attack (a some what slow, moderately damaging ranged attack) fire off a torrent of missiles, an attack which is given away by multiple targeting lasers. It’s also not above simply whacking you with its gun in melee, either. Despite their size, they’re not quite as sturdy as you might think.
Kill your foes and make your way to the shuttle platform (the western-most of the two launch platforms here) and destroy three more caches to end the threat to Prodromos. For whatever reason, Kadara’s viability will increase (29 AVP, +2% Kadara viability and 270 XP) for this. You’d think Eos would benefit, given the nature of the threat, but… hey, rewards are rewards. Before you leave, search the area to find an Adaptive Remnant Core Device under the eastern landing platform.