I have been doing this manually, but I believe there should be a way to handle this for multiple layers at once. How can this be done?
Simple answer; select all the layers.
Hitting T (the shortcut for "Opacity") with multiple layers selected will bring up the "Opacity" for all those layers. Any changes you make will be applied to all the selected layers; including adding keyframes and changing values.
Inputing an exact value will set all the layers to that specific value. Dragging the value will adjust all the values relatively from their current value.