欧博娱乐English Language & Usage Stack Exchange
About 150 years after Shakespeare published the sonnet under discussion here, Samuel Johnson, A Dictionary of the English Language (1756) included these definitions of slut and sluttish:
SLUT, s. {slodde, Dutch} 1. A dirty woman. King. 2. A word of slight contempt to a woman. L'Estrange.
SLUTTISH, a. Nasty; not nice; not cleanly; dirty; indecently negligent of cleanliness. Raleigh.
Evidently in Shakespeare's time slut and sluttish were understood in much the same way that slattern and slatternly were—as referring to a person (usually a woman) who paid insufficient attention to cleanliness. Sluttish might therefore also be associated with notions of unkemptness or slovenliness, as well as of actual dirtiness. Obviously, these are not actual characteristics of time, understood as an abstract though measurable entity. And yet "sluttish time" isn't a metaphor for time; a metaphor would be something like "sluttish drab" standing in for "time" (if drab is used in one of its two early senses of "slattern" or "prostitute").
In a comment beneath Joe Blow's answer, the poster provides a definition of transferred epithet, a term I was not familiar with:
A transferred epithet often involves shifting a modifier from the animate to the inanimate, as in the phrases "cheerful money," "sleepless night," and "suicidal sky."
Given the close connection of slut and sluttish with specifically human (and more specifically female) hygiene, I think it is fair to say that "sluttish time" qualifies as a transferred epithet, as the poster defines that term. "Sluttish" would perhaps be even more obviously a normally animate modifier if it meant "indiscriminately promiscuous," as it does today. "Sluttish time" may also qualify as personification, depending on how you define that term. Merriam-Webster's Eleventh Collegiate Dictionary (2003) has this as its primary definition:
personification n 1 : attribution of personal qualities; esp : representation of a thing or abstraction as a person or by the human form
In the sonnet, Shakespeare attributes a personal quality (sluttishness) to time, but he does not represent time in human form (as he might have done with a phrase such as "that sluttish fishwife, time"). It therefore seems to me that of the terms suggested by the poster—metaphor, transferred epithet, and personification—the one that best fits "sluttish time" is transferred epithet.