How does Shakespeare's Sonnet 130 mock the Elizabethan sonnet tradition?

By the time that Shakespeare came to write Sonnet 130, the traditional Petrarchan love sonnet was starting to look pretty worn-out. It seemed that poets, even the very best ones, had exhausted all the possibilities of the form. In particular, the language used in such poems had become cliched, with the same words being used over and over again in comparing the beauty of the speaker's beloved to the beauties of nature. (Lips would be "ruby-red," skin like "alabaster," and so on.)

Throughout Sonnet 130, Shakespeare compares his beloved's beauty to a host of features from the natural world. Nothing particularly original here, one might think. But crucially, Shakespeare turns the old love sonnet conventions upside-down by acknowledging that such comparisons do not redound to the benefit of his beloved. Her eyes are nothing like the sun, her lips aren't as red as coral, and so on. It almost seems as if the speaker is mocking his lover as well as the established conventions of Elizabethan love sonnets.

But this impression is dispelled by the last two lines of the poem, the couplet, in which the speaker says that none of these unflattering comparisons with nature ultimately matter. For he knows that nothing can compare to his beloved:

And yet, by heaven, I think my love as rare

As any she belied with false compare.

What type of poetry is mocked in Shakespeare's Sonnet 130?

Shakespeare's Sonnet CXXX mocks the Elizabethan conventions of poetry that extolled ideal love as well as satirizing the Petrarchan sonnets that compared the object of love to Nature in hyperbolic terms. For, instead of making such flattering comparisons, Shakespeare's speaker places his lover in contrast to the beauties of nature and parodies the lofty language of courtly love.

My mistress' eyes are nothing liek the sun
Coral is far more red than her lips' red;
If snow be white, black wires grow on her head
I have seen roses damask'd, red and white
But no such roses see I in her cheeks....

Authorities believe that the "roses" are allusions to the red and white roses that the House of Tudor adopted as its symbol in the War of Roses, further mocking the exaggerated "false comparisons" of Shakespeare's speaker. Also, in comparison to Sidney's Astrophel and Stella and its courtly love which Shakespeare parodies, the reader can easily detect the elements of the conventional love sonnet as, instead of comparing his love to Venus, Shakespeare speaker writes, instead, of the humanity of his lover who "treads on the ground." Yet, Shakespeare's speaker finds her love rare and treasures it. 

What conventional images does Sonnet 130 ridicule, and which poems is Shakespeare mocking?

In Shakespeare's Sonnet 130, he is listing the attributes of the woman he loves, but not in a necessarily positive light. He speaks of her looks (her eyes, her lips, etc.) and points out what they are not.

My mistress' eyes are nothing like the sun;

Coral is far more red than her lips' red...

The speaker goes on to note that her hair is like wire, her cheeks are not lovely and her breath "reeks." Though he loves to hear her talk, music is much more appealing than the sound of her voice:

If hairs be wires, black wires grow on her head.

...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...

In listening to these first two and a half quatrains, we might think that the speaker's "mistress" will not be pleased with his poetic efforts: his relationship may be over before she reaches the end of her sonnet. However, the last two lines of the third quatrain introduce an observation that puts all of what he has written before, into its proper context: how can he or anyone else compare his love to a "goddess," when no one has ever seen one? In essence, he might well be saying that she is a goddess as far as anyone else truly knows.

This brings us to the second part of your question—the kind of poem Shakespeare is ridiculing: he is making fun of love poems that make impossible comparisons with creatures they know nothing about. If goddesses do exist, a woman cannot logically be compared to one because no man has ever seen one in order to make a fair and valid comparison in the first place.

Shakespeare ends his sonnet by praising his lover on his own terms, not based on false allusions:

This is what Shakespeare means by “false compare”—unjust comparisons that not only ignore the possibility that the woman may be beautiful in her own right, but also miss the value of the beloved in the eyes of her lover...

Shakespeare finds that everything about his mistress is lovely to him and "rare." Rather than using empty praise to describe this woman, he uses logic instead which is objective rather than subjective. His descriptions are in no way meant to discredit her, but simply to put the process of praise in perspective. Comparing a woman to an unknown quantity is as effective and "honest" as comparing her hair to wire or saying her breath "reeks." An unsubstantiated comparison is meaningless to the speaker.