How can I demonstrate that Prometheus Unbound is a romantic poem?
The easiest way to define Percy Bysshe Shelley's poem Prometheus Unbound as a Romantic poem is to look at the poet himself.
P. B. Shelley was a Romantic poet. His works were those typical of the movement based upon the fact that he wrote with language filled with references to nature. Shelley was simply an idealist (to the point of being heavily criticized--most notably by Mark Twain).
As for the poem, Prometheus Unbound, one can easily see Shelley's attention to detail regarding the natural elements surrounding Prometheus. Prometheus was bound to a cliff, by Jupitor's order, given Jupitor's jealousy of his power. For thousands of years, the Titan was beaten by nature itself (his heart being eaten, repeatedly, by an eagle and the elements of nature itself).
Overall, Shelley's intent for the poem was to show the power which individualism and intuition has on a person. Both of these themes were very important to the Romantic.