To say that Shelley's "Triumph of Life" was influenced by Dante's The Divine Comedy is somewhat analogous to claiming that The Divine Comedy was influenced by the Bible. He is toying with the same ideas and concepts, and much of his imagery is lifted straight out of Dante. One might question, however, how someone whose philosophy is so very nearly completely opposite that of Dante could admire his work so much, and it would be a cheap, although possibly not inaccurate, response to say that Shelley appreciated finding a poet with an ego to match his own. Shelley, then, much as Dante himself did with his influences, took the parts he liked and rearranged or discarded the rest.
"Triumph of Life" is set in what appears to be the earthly paradise, only it's not such a happy place. The triumphal pageant is more reminiscent of the "indifferents" in ante-hell than anything found in Dante's Paradiso. Shelley (and, one might add, the romantics in general) places greater importance on individualism, and less on community. Consequently, the forgetfulness of the waters of Lethe is disturbing, rather than comforting. In lines 469-480, he references Dante directly, and claims that Dante could explain everything except Love; a bold claim to make about a poem whose very center is the word "amor." In 511-516, Shelley echoes Inferno 14, although Shelley is all pity for the "sinners." Indeed, he never claims that any of the persons he is describing are sinners at all. Perhaps most telling of Shelley's dissents, though, is in lines 128-129, where he says, "All but the sacred few who could not tame/ Their spirits to the conquerors." Even besides the romantic ideology that is positively dripping from these lines, one can't help but feel that Shelley's unnamed "sacred few" could not possibly have made it higher in Dante's cosmology than the eight circle of Hell.
Both "Triumph of Life" and "Ode to the West Wind" are written in terza rima, which was invented by Dante for The Divine Comedy, although "Ode to the West Wind" is actually a terza rima sonnet form, but Shelley uses this in a very different way than Dante does. Whereas Dante typically completed a thought or idea within a terzina, or even a line, Shelley splays all over the place. He steadfastly refuses to put a period at the end of a terzina, and his dangling sentence fragment splunge the reader head first into the next one, and so on.
"Ode to the West Wind" is less obviously taken from Dante, although the influence is still apparent. The line, "So sweet, my sense faints picturing them!" could have been lifted verbatim from almost any canto in the comedy. The headstrong, all-or-nothing tone of the metaphors in this poem are very much in keeping with Dante, but the primal force behind them is, for Shelley, more physical than spiritual. The imagery of this poem also recalls Inferno 1, but Shelley needs no spiritual guide out of his dark wood; the natural forces of the universe will, he concludes, lead him out of it in time.
Another poem by Shelley that shows Dante's influence is "England in 1819." Here Shelley, much like Dante, is concerned with the politics of his country, and the unhappy state of current affairs. The poem could, perhaps, be re-titled "Florence in 1300," and one cannot imagine that Dante himself would have hesitated to sign his name to it. Furthermore, the much-awaited two-line predicate of this sonnet-sentence rather forcefully recalls Inferno 10, with Farinata rising out of his tomb. The final irony of this illusion is tht Shelley's "glorious Phantom" is Dante's heritic, damned to suffer in hell for all time.