How would one prove that "The Eagle" is not a mere description of an eagle?

First, the eagle is personified, described as having "hands," and this is a big clue that he represents more than just an eagle (line 1).  In addition, the fact that his hands are described as "crooked," a word with two pertinent denotations, is another clue: "crooked" can mean "bent" (as an eagle's talons would be) as well as "corrupt" (as an unethical or immoral person would be) (1).  Further, the eagle is described as "stand[ing]" and "clasp[ing]" instead of perching, two more word choices that hint at his power and strength (especially compared to the "crawl[ing]" sea in the second stanza) and suggest that he is not just a bird.

Moreover, the description of the sea as "crawl[ing]," a movement associated with the weak or powerless, helps to show that this is, ultimately, a poem about power: who has it, how they keep it, and who doesn't.  Finally, the speaker says, in the last line, that the eagle "falls," not that he dives, and this compels us to consider the poem as a comment on absolute power and, perhaps, how it changes hands (6).

Therefore, by choosing words that more often describe human features or activities, Tennyson forces us to reflect on the way in a human being could acquire and exploit absolute power, as the eagle does.