Can somebody please tell me what is the extended metaphor of Shakespeare's Sonnet 100?
Well, to be precise, this sonnet does not actually contain an extended metaphor. Let us remember that an extended metaphor is a metaphor that is continued and developed throughout the course of a poem or a passage. In this poem, no such extended metaphor is used. Instead, Shakespeare personifies his inspiration as an external body or force, entitled "Muse," and asks it why it has apparently abandoned him for so long:
Where art thou, Muse, that thou forget'st so long
To speak of that which gives thee all thy might?
Spend'st thou thy fury on some worthless song,
Darkening thy power to lend base subjects light?
The poem is thus an imprecation for the Muse, or the speaker's inspiration, to return to the speaker so that he may once again set about his most important task, which is setting down the beauty of his beloved so that he can remove the object of his affection from the ravages of time for all eternity by capturing his love and beauty in verse form:
Give my love fame faster than Time wastes life;
So thou prevent'st his scythe and crooked knife.
Thus this poem contains no extended metaphor, but rather personifies the poet's inspiration so as to help us understand how he has lost his inspiration to continue writing about his chief objective.