Sonnet 130 doesn't present or discuss a traditional conflict; rather, it satirizes typical romantic poetry of the time, specifically the kind that used hyperbolic language to describe a subject's beauty. Shakespeare pokes fun at this common poetic method by doing the opposite: describing the "mistress" in the poem by comparing her appearance, breath, and voice unfavorably to traditionally beautiful things like roses, snow, music, and goddesses:
My mistress' eyes are nothing like the sun;
Coral is far more red than her lips' red;
If snow be white, why then her breasts are dun;
If hairs be wires, black wires grow on her head.
I have seen roses damasked, red and white,
But no such roses see I in her cheeks;
And in some perfumes is there more delight
Than in the breath that from my mistress reeks.
I love to hear her speak, yet well I know
That music hath a far more pleasing sound;
I grant I never saw a goddess go;
My mistress, when she walks, treads on the ground.
The woman Shakespeare describes has lips that are not particularly red, skin that isn't snow-white, cheeks that aren't rosy, breath that is not sweet, and a voice that is not musical. The sonnet ends on a favorable note, however:
And yet, by heaven, I think my love as rare
As any she belied with false compare.
It could be said that the conflict in the sonnet is that the woman being described does not measure up to these elevated standards of beauty, but Shakespeare presents the idea in a clearly satirical way.