There are lots of rhetorical devices to be found on the opening page of this story, including allusions, metaphors and similes.
There is an example of an allusion at the very beginning of the story. The narrator says, "The Wandering Jew? - certainly not." This is an allusion to a legend about a Jew who, as a punishment for mocking Jesus before the crucifixion, was made to wander the earth for all time. The point of the allusion is to emphasize the narrator's claim to immortality. The allusion also gives to the story, from the beginning, an ominous tone. We perhaps wonder whether the narrator is guilty of something as appalling as that for which the Wandering Jew was punished, or whether he perhaps suffers as much as we suppose the Wandering Jew does.
Also at the beginning of the story, the narrator uses a metaphor, when he laments the "weight of never-ending time." The narrator claims to have lived for "three hundred and three years," but these years of course do not literally exert a weight upon the narrator. The metaphor does convey, however, just how burdensome an immortal life can be, and seems to have been for the narrator.
In the subsequent paragraph, the narrator says that the memory of Cornelius Agrippa is "as immortal as his arts have made me." Cornelius Agrippa was a sixteenth century philosopher, theologian and alchemist. He also exerts a considerable influence upon Victor Frankenstein, Shelley's most famous character. When the narrator in "The Mortal Immortal" contends that he is "immortal" because of the "arts" which Cornelius Agrippa has made for him, he means that Agrippa has used his knowledge of alchemy to make for him an elixir which has made him immortal. The narrator implies that he will now live forever, as will the memory of Cornelius Agrippa.