The term 'eagle-eyed' is an idiom used to describe someone who is very observant and has a keen eye for detail. This can be seen in the two crossword solutions, 'ASTUTE' (6 letters) and 'ALERT' (5 letters). ASTUTE means having or showing an ability to accurately assess situations or people and make good judgments, while ALERT means being watchful and quick to notice any danger or problems. Therefore, the term 'eagle-eyed' implies someone who is both ASTUTE and ALERT, able to quickly identify potential issues and make sound decisions.