In this poem, the titular "passionate shepherd" is describing to his love how he will deck her in glorious array made only from nature. The shepherd is not a wealthy man, and, as such, the riches he offers to his love are drawn from the beauty of the nature which surrounds him.
The "melodious birds" in his natural world "sing Madrigals" to serenade the "falls"—but, as a madrigal is a very complex polyphonic type of choral music, we can understand that this is a metaphor indicating that the birds sing beautifully. They are not really singing madrigals, although the image of them serenading the falls is an example of personification. Likewise, the "kirtle" he offers will not really be "embroidered" with "leaves of myrtle"—the embroidery is metaphorical; the suggestion is that myrtle leaves will form some kind of decoration for the kirtle.
This poem is heavily laden with imagery, but I'm not sure whether there are many more outright metaphors in it. When the shepherd says that he will make his love a "belt of straw and Ivy buds," he may be making the belt out of unconventional materials, but will it still be a real, rather than a metaphorical, belt? Arguably, yes, as there is no requirement that a belt be made of leather or cloth. It is perfectly possible to make a belt out of these materials which would span the lover's waist, just as a crown of thorns is still a crown, albeit not one made of gold. It isn't metaphorical, like saying that someone is "crowned in glory." The same could also be argued of "beds of Roses." In this instance, the speaker is saying he will make a bed for his love out of roses; it will not literally be a bed as we might understand it, with mattress and pillows, but will serve the same function. So, isn't it really, rather than metaphorically, a bed? In large part, it seems that the shepherd's attempts to lure his love are not based in offering metaphorical delights, but in explaining how comfort can be provided to her through the bounty of nature; not, perhaps, in the ways she has been used to, but in ways which will serve just as well.