Simplicity and detail are key. So remain focused on the 1) "good" bald eagle, 2) "evil" bald eagle, 3) American flag that rests in their claws, 4) clouds and 5) "MASTER YOUR ART" in Korean translation.
Try to make these elements fit smoothly together. Make the eagles fit appropriately with the headband. Remember, these eagles are in battle with each other, so make them look the part! Have them with cuts, bruises, blood, scars and etc. on their bodies to show the great battle that they are in with one another.
Although I am pretty specific with what I'm looking for, don't be afraid to step outside of the box and use your imagination to add some spice and flavor. Who knows, maybe a lightning rod could look really cool in this design- I don't know.
I do know what the main necessities are, but feel free to add some stuff of your own. Hey, the worst case scenario is that I ask for you to remove it- but still, you could potentially win the contest :)