After meeting up with the Duke in the Altar area, you’ll find a bunch of treasure chest icons on your map. These are all optional treasure, guns, and weapon upgrades you can track down between ...

A silver treasure chest icon indicates that bric-a-brac has been detected, while a gold treasure chest icon indicates that treasure is in the vicinity. —Monsters sensing bric-a-brac.

Go over to the icon's location to loot your rewards. You'll also see four treasure chest icons at the top of your screen, which indicate your current progress in the Plunder.

I’ve provided a map screenshot below with the approximate co-ordinates and exact Zora Spear location marked with a treasure chest icon below, so I’d recommend marking the same spot in your map ...

In both cases, you'll have to get pretty close. Look for the treasure chest icon and listen for the beeping of the switches to find which doors have unlocked in the Castellum.