To get in the eagles nest, you need to use the teleporter on the side of the mountain across the bay. It's on the island mountain between the two fjord entrances (not the one you enter the area through) and will teleport you to the base of the ladder. Once you get up into the lower level you have to defeat both of the opponents to get access to the upper level where there are levers to turn off all the barriers in the local area.
