Location: Rymasov Flat
Petitioner: Wounded Republican Soldier
Unlocked: Complete Things Fall Apart
Reward: 100 Magicked Ash, 1 Meteorite, 25 Renown
In order to unlock this side quest you need to more or less complete Things Fall Apart, a main story quest with three sub-quests attached. Once you've completed the three sub-quests and reported back to Otto at the Hideaway you can begin several side quests. Visit the Krzjit Echoes at least once and Bad Blood will appear on the map.
Make your way through the Krzijit Echoes to the Rymasov Flat and you'll find a Wounded Republican Soldier, just before the path widens into a larger area. The soldier was hurt by his own men, all turned Akashic, and he worries that the aetherflood which swallowed his camp will demolish the nearby village of Tabor.
You'll find the encampment in the north of the Rymasov Flat, on your left as you enter the open area of the flat. Enter the encampment and you'll find it filled with Akaschi Steeds and Akashic Scimatars. They're basic enemies that won't give you much trouble. Take the whole group out to receive Sharp Fangs, Bloody Hides, and Magicked Ash.
One the Akashic are gone you'll hear someone calling for help. If you check the northeast of the camp you'll find a broken bridge, and near it is a Dying Republican Soldier. Speak to him to complete the quest... and to receive a choice. Which option you choose doesn't really matter, aside from changing the cut scene a bit.