This ultimate magnum gun can be located at the Balouve Mines secret area - the same place where you’ve found Apocalypse greatsword.
To employ the Armiger Arsenal you'll first need to charge it up adequately. I did it with the Thunder Bombs near the Malmalam Thicket (used a LV1 Thunder, de-aggroed the bombs, waited for the cooldown and started over) and got around 500k exp from 20 Lv1 Thunder w/ Expericast lv 96 with a Moogle Armlet.
Chamber of First Light Final Fantasy 15 is divided up into many chapters, each of which span large areas to explore, and both main and side quests to undertake.