How do we know that the hunt is not just, say, a jolly ride through the fields? This adjective is our key. A "cruel bugle" blowing becomes something like a synecdoche for the person blowing the bugle—the hunter.
the famished arrow sang (20)
Since when are arrows hungry? When they're described using personification, that's when.
Paler be they than daunting death the sleek slim deer the tall tense deer. (26-28)
Woah. Whenever death shows up in a metaphor, chances are that things are about to take a turn for the worse, and fast. It's the literary equivalent of putting a target on a character—or, in this case, a deer.
My heart fell dead before. (31)
What a turnaround! The poem may not have the form of the sonnet, but it sure presents the same surprises that the sonnet usually saves for the last two lines. In this case, the violence gets re-directed, away from the deer and toward the rider ("my love" ), who gets described here as "my heart."