Early in the story, the narrator foreshadows the tragic end that awaits Giovanni and thus heightens the story's atmosphere of Gothic horror. After Giovanni's first conversation with Beatrice, which leaves him troubled and apprehensive, the narrator observes:
The wisest course would have been [...] to quit his lodgings and Padua itself at once; the next wiser, to have accustomed himself, as far as possible, to the familiar and daylight view of Beatrice [...]. Least of all, while avoiding her sight, ought Giovanni to have remained so near this extraordinary being that the proximity and possibility even of intercourse should give a kind of substance and reality to the wild vagaries which his imagination ran riot continually in producing.
Here, the narrator's cautionary notes suggest that Giovanni should have ceased to pursue his curiosity about Beatrice as soon as he began to suspect that something was awry. Notably, the narrator's warning takes the form of a list of three that starts with the "wisest course," proceeds to the "next wiser," and ends with what Giovanni should have done "least of all"—which, of course, is the path he ultimately chooses. This triadic structure heightens the reader's sense of impending doom. In this way, the story shows the reader that Giovanni has chosen unwisely—and foreshadows the doom that awaits Giovanni and Beatrice after the former succumbs to his curiosity.
After Baglioni warns Giovanni about Rappaccini’s immorality and his professional stature as a scientist, the narrator uses dramatic irony to foreshadow Baglioni's cruel machinations at the end of the story:
[Giovanni] might have taken Baglioni's opinions with many grains of allowance had he known that there was a professional warfare of long continuance between him and Dr. Rappaccini, in which the latter was generally thought to have gained the advantage. If the reader be inclined to judge for himself, we refer him to certain black-letter tracts on both sides.
Here, the narrator gives the reader a key piece of information that Giovanni lacks—namely, that Baglioni’s condemnation of Rappaccini is rooted in jealousy. As a result, his assessment of Rappaccini is likely to be biased. In the hopes of bringing down his professional rival, Baglioni has a motive to harm Beatrice, and Giovanni is completely unaware of this dynamic. As a result, the dramatic irony here leads the reader to suspect that Baglioni is plotting something—and that Giovanni will fail to anticipate it. Moreover, the narrator’s observation that Giovanni “might have” acted differently had he been given this information reveals to the reader that he will make a fatal error due to his ignorance. This heightens the ominous mood of the story and foreshadows its tragic ending.
When Giovanni first comes across Rappaccini's garden, the story calls attention to a statue of "Vertumnus," which is an allusion to the god of change and the seasons in Roman mythology:
One plant had wreathed itself round a statue of Vertumnus, which was thus quite veiled and shrouded in a drapery of hanging foliage, so happily arranged that it might have served a sculptor for a study.
In Ovid's Metamorphoses, Vertumnus seduces a wood nymph, Pomona, by disguising himself as an old woman in order to gain her trust, enter her orchard, and convince her to marry him. Like Pomona, Beatrice is a young woman who is very much in touch with nature, as she's devoted to caring for the plants in her garden. Both women are enclosed in a natural haven that excludes men. Like Vertumnus, meanwhile, Giovanni inveigles his way into this haven and seduces the woman he desires.
By drawing these parallels between Beatrice and Pomona (and between Giovanni and Vertumnus), this allusion foreshadows Giovanni's seduction of Beatrice. Of course, unlike the story of Vertumnus and Pomona, in which the former's deceit culminates in a happy marriage, the story of Giovanni and Beatrice ends in misfortune and tragedy.
"Rappaccini's Daughter" can be read as an allegorical representation of the biblical Fall of Man. Rappaccini's garden resembles the Garden of Eden in many ways: it is a beautiful and bountiful garden, populated by one man and one woman—that is, Giovanni and Beatrice. In the biblical narrative, Eve tempts Adam into sin by eating the forbidden fruit. Likewise, Giovanni succumbs to the temptation of Beatrice's beauty and becomes poisonous himself.
However, "Rappaccini's Daughter" turns this story on its head by shifting responsibility for the Fall from Eve to Adam: it is Giovanni's failure to resist his curiosity about Beatrice that provokes his downfall, and it is his reliance on reason rather than intuition that subjects the innocent Beatrice to undeserved pain. Beatrice's final suggestion that there was "more poison" in Giovanni than in herself cements the notion that Giovanni is responsible for the Fall, not Beatrice.
It is notable that the narrator makes explicit reference to the story of Adam and Eve early in the story when Giovanni watches Rappaccini tending to his garden, though the story presents Rappaccini (not Giovanni) as Adam:
Was this garden, then, the Eden of the present world? And this man, with such a perception of harm in what his own hands caused to grow—was he the Adam?
The fact that the narrator presents this comparison as question suggests that Giovanni, not Rappaccini, is actually the one who's comparable to Adam—but he doesn't know this yet. This foreshadows the ending of story, in which, like Adam (who succumbs to his curiosity), Giovanni sparks his own downfall.
Using similes, the story repeatedly compares Beatrice herself to the flowers of the garden. Watching Beatrice tend to the garden, Giovanni thinks she resembles them:
[...] for the impression which the fair sister made upon him was as if here were another flower, the human sister of those vegetable ones, as beautiful as they, more beautiful than the richest of them, but still to be touched only with a glove, nor to be approached without a mask.
The similes in the passage above not only compare Beatrice to the flowers in the garden in terms of her beauty, but also insinuate that she is just as toxic as they are. The simile comparing her to the "human sister" of the toxic flowers further highlights the notion that Beatrice resembles the flowers not just superficially, but at a fundamental level.
The story further accentuates this comparison through metaphors. In the same scene, Giovanni "almost doubted whether [Beatrice] were a girl tending her favorite flower, or one sister performing the duties of affection to another.” Again, this metaphor suggests that the toxic flowers are Beatrice's kin. These comparisons between Beatrice and the plants of the garden foreshadow the revelation that her body is poisonous.