Few tricks I've found:-
1. -Detection Radius helps a lot, since the sight-lines you get are handy warning to loose a big attack off on their approach / dodge them.
2. Ground-sliding attacks are also handy since they stick around and so have a chance for the eagles to run into them.
3. I haven't tried this one, but apparently beartraps are also handy as obstacles to catch them in.
4. The top level is better if you want to try a dodging-based strategy, while the ground level is better for actually killing eagles (since you then have flatter ground to work with.)
5. If you have a decent enough constant output spell (flamethrower and geyser come to mind, it will generally catch eagles for some damage as they go past; this is probably your last resort, though, since you will almost certainly be taking damage this way.