The speaker uses frequent parallelism and anaphora (which is a specific kind of parallelism) in order to build her argument.
Take lines 2-3, for example, which follow the same general structure as the speaker tells her beloved not to do something mourning-related on her behalf:
Sing no sad songs for me;
Plant thou no roses at my head,
That parallelism makes the lines feel all the more insistent: the speaker isn't being coy, but truly doesn't want her "dearest" to do these things.
Lines 7-8 contain more parallelism, as the speaker repeats the phrase "And if though wilt" at the start of each (an example of anaphora):
And if thou wilt, remember,
And if thou wilt, forget.
This anaphora draws attention to the repeated phrase, emphasizing the fact that the speaker doesn't care so much whether or not her loved one remembers or forgets her; what she cares about is that this person does what is best for them. Their "wil[l]," or choice, is what matters to her.
The next three lines feature yet more anaphora and parallelism. The speaker opens each line with the statement "I shall not," which is then followed by a sensory verb ("see"/"feel"/"hear") and a noun drawn from the natural world:
I shall not see the shadows,
I shall not feel the rain;
I shall not hear the nightingale
The repetition of "I shall not" again feels insistent; the speaker is trying to convince her loved one that she won't be around to notice anything that they do after she dies. These lines also reiterate the sense of disconnection that the speaker believes is part of death. Her earthly senses won't be working.
Finally, the poem echoes the first stanza's closing lines in those of the second. Again, the speaker opens each line with a repeating phrase ("Haply I may"/haply may"). Like "And if thou wilt" from the first stanza, this phrase implies that forgetting/remembering isn't entirely within the speaker's control, and thus not worth worrying about: maybe she'll remember, and maybe she won't—she just doesn't know!