To beat the eagles (which, I'm pretty sure, isn't a bird that eats insects :o) place yourself just above just above the clouds, and prepare to dodge either by going up or down, and replace yourself. That's one of the safest spot.
The game is great, fits the theme perfectly imo, the different gameplay loops are (too?) short but complete, and the game being story focused isn't hard (apart from the final stage). Nice job :)