Eagle is a Green Earth CO, boasting strong Air units as well as one of the strongest Super CO Powers in the game.
Eagle is an aerial-only specialist; however, the real threat he poses in the battlefield is his Super CO Power, Lightning Strike, which gives all non-footsoldier units an extra turn. Even though he has pretty bland land units, Lightning Strike makes said units deadly enough to beat most COs with better unit stats.
He pays for his really strong Lightning Strike with a very long Power bar, and relatively weak 100/100 land units.
Eagle has arguably the strongest Super CO Power in the game, but his units are relatively weaker day-to-day; what he'll have to do, generally, is survive with enough units. The easiest way to do this is to play more defensively.
Avoid trading off units, retreat when you have to, maintain a strong frontline at all times, whatever, as long as Lightning Strike will be active on enough units. It's fine to lose some ground and 1-2 cities, a good Lightning Strike will usually recover them; just don't lose too many units.
Building a B-Copter or two helps a lot more if playing as Eagle; they trade really well against other air units, forcing the opponent to counter with an Anti-Air instead of the usual B-Copter. They also give at least one star of charge when destroyed (including the damage dealt by the copter before it gets destroyed), so you'll be able to get the Lightning Strike earlier. Don't go overboard though, or Anti-Airs will ruin their day.
On the day you get to use Lightning Strike, make sure:
- Enemy units are vulnerable (don't use it if the opponent has retreated a long way)
- Powers like Olaf's Blizzard, Sonja's Counter Break, Javier's Tower of Power, Lash's Prime Tactics, etc. aren't active (Basically avoid anything that limits movement or increases enemy defense significantly)
- It's used after all vehicles, air units, and naval units have moved, but before moving footsoldiers (Footsoldiers do not move again during Lightning Strike, but get the usual 10% increased offense and defense during CO Powers anyway).
Don't forget that the mere threat of Lightning Strike can send entire armies on the retreat; it can be beneficial to delay it a little and advance into areas the enemy cannot cover anymore.
How to Counter
Sasha naturally counters COs who rely more on their powers; Market Crash can easily wipe out half a CO's power bar and will crash COs like Eagle to the ground.
Aside from that, it's easy to pressure him with a CO with superior day-to-day abilities, like say, Von Bolt. Go on the offensive early; contest cities, trade units, zone him away. The point is to force him to lose a lot of units, or lose a lot of ground (like more than he can handle) if he doesn't oblige. Never let him build walls of units in the process so he cannot defend well.
Go all out right before and right after the Lightning Strike, if possible. If his army takes a hard enough hit, it wouldn't matter if he moves twice; damaged units deal less damage and take more damage in return.