A metaphor is a figure of speech wherein the words used cannot be literally applied to the thing they are describing. Figures of speech are commonly used and the most popular ones include simile, metaphor, personification and hyperbole, although there are many more; all of which create a special effect. Metaphor is an imaginative way of creating a visual picture through comparison but without the need for the words "like" or "as" (which would make it a simile) to complete the comparison.
There is a very good reason why the metaphor and idiomatic expression referring to someone's "eagle eye" exists. Eagles can spot small animals over long distances and their eyesight is several times stronger than the average human being. The clarity and color of an eagle's vision is also far superior and those people with excellent vision and many long-sighted people are said to have an "eagle eye" due to their ability to spot small objects or almost indistinguishable images from far distances.
Ask the question. Does the thing you are describing actually have "the eyes of an eagle?" Does the reference create a visual picture of someone or something with exceptional eyesight where his, her or its eyesight is so good that it could be compared to the eyesight of an eagle? If you are describing, for example, your cat and have noticed how it can spot a small bird from an exceptionally far distance, far more than the average cat, never losing sight of it, you are using the words metaphorically. Therefore, to say that something has "the eyes of an eagle" is to use a metaphor, creating that visual image of eyesight far superior to what would usually be associated with, to use the earlier example, your cat.
In my opinion, I think this phrase is definitely a metaphor because it makes a comparison by stating that 'it' has the eyes of an eagle. This implies that the 'thing' that is being compared has a keen and watchful eye. IT doesn't let anything out of its sight. Nothing can escape it. The sense of observation and insight of this thing is keen and acute. Every movement is scrutinized closely. Trying to escape the eye of this thing would be almost futile.
Other ways of saying the same thing would be:
It has eagle-eyes. (Metaphor)
Eyes like an eagle. (Simile)
Hope this helps answer your question.