Work in Progess
At Corto Cay, QUITO is a closed tower with 2 grapple points.
Climb up the first grapple point, take the ladder and walk the wooden boards to the very end.
There is a bit of wooden board that goes a bit outside the tower. Go as far as possible without falling.
From here you can grapple to the second grapple point, climb up and claim the weapon.
TORRE DEL LEON, OLD PUEBLO, ESPERANZA.
Build a Level 2 Hunter's Lodge.
The shotgun is at the GDP OIL PLATFORM, COBRE SHORES, AGUAS LINDAS.
It's inside a blue container. The entrance is blocked by another blue container.
To move the container that is hanging on the crane, you have to find the crane controls.
They're in the west inside the control room (see screenshots for location)
While doing the RADIO LIBERTAD Operation Mission at Noventarmas, where you have to blow up the satellite dish, you can find this chest at the top of the tower.