[@Raijinslayer] - Hm, well, I wouldn't suggest letting any part of the body being caught by an Esper Ridge Eagle's mouth, they have a pretty nasty set up with their beaks; jagged and have teeth spanning down their throats that impales and cuts up their prey when they swallow them whole - usually alive - and can expand their jaws wide similar to a snake. They crush opponents with their talons, pinning them in place or grabbing them in a vice in order to hold them still so they can be taken in one go. 

But, the most dangerous weapon they have are their wings - they use those for their Phantasm and their element attack: Vile Gust.

If you went that route with James, the Eagle would attempt to swallow him whole, rather than bite off an arm, their intellect is enough that they recognize an armoured opponent, so they'd attempt to get rid of them without snapping down - I imagine the Cerburus Armour would be strong enough to withstand the beak snapping closed and a predator like the Eagles wouldn't want to risk that. 

You could go either route in this, honestly, I leave the battle posts to your creativity. Maybe look up the image of an eagle's skull to get a reference if you plan to remove the eye in the original way you intend?