Copy and paste from some website:
First – This one is located in the very first cave you fall in when you start the game and are playing as young Aloy. You can only find the item as an adult, so you will have to revisit the location. It's directly east of Mother's Watch, which is in the southeast area of the world map. Drop into the cave and continue through until you come across a passage blocked by sharp, breakable rocks. It will be sitting on a desk.
Second – You'll have to advance at least up to the Womb of the Mountain quest which allows you to explore All-Mother Mountain. As you make your way through, without advancing the mission, you'll find a locked door with a bright red circle on it. You can't open it, but if you look to the left of this area you'll find a tunnel that will lead you to the next cell for the ancient armory. If you didn't get it during this quest, you can return to this area later, after progressing further in the story.
Third – To obtain this next one you'll have to make it up to the Maker's End quest in Horizon Zero Dawn and climb the Faro Skyscraper (this can be done after the quest as well). You will find it all the way at the top after learning about the lady that looks like Aloy. Just look for another path after that scene and you'll be able to go even higher.
Fourth – This one is found during or after the Grave-Hoard quest (which is after the Maker's End quest). When you reach the main area of the ruins, scan your surroundings to find this power cell laying about.
Fifth – The final Power Cell needed for the Ancient Armory quest is found during the quest The Mountain That Fell. During the quest, you'll come across a hologram that shows Faro talking with scientists working on GAIA. As you progress past that point, there will be a zipline that you need to ignore for a moment. Look around and you'll find a passage to a cave nearby that leads down to a Power Cell. Now you can return to the zipline and continue the quest.
Second – You'll have to advance at least up to the Womb of the Mountain quest which allows you to explore All-Mother Mountain. As you make your way through, without advancing the mission, you'll find a locked door with a bright red circle on it. You can't open it, but if you look to the left of this area you'll find a tunnel that will lead you to the next cell for the ancient armory. If you didn't get it during this quest, you can return to this area later, after progressing further in the story.
Third – To obtain this next one you'll have to make it up to the Maker's End quest in Horizon Zero Dawn and climb the Faro Skyscraper (this can be done after the quest as well). You will find it all the way at the top after learning about the lady that looks like Aloy. Just look for another path after that scene and you'll be able to go even higher.
Fourth – This one is found during or after the Grave-Hoard quest (which is after the Maker's End quest). When you reach the main area of the ruins, scan your surroundings to find this power cell laying about.
Fifth – The final Power Cell needed for the Ancient Armory quest is found during the quest The Mountain That Fell. During the quest, you'll come across a hologram that shows Faro talking with scientists working on GAIA. As you progress past that point, there will be a zipline that you need to ignore for a moment. Look around and you'll find a passage to a cave nearby that leads down to a Power Cell. Now you can return to the zipline and continue the quest.
