Hughes uses repetition, alliteration, and syntax in this poem to suggest the elemental power of the hawk. This language turns in on itself and, in a sense, becomes about itself; in this sense, Hughes is not writing about a hawk at all, but his own hawk-like prowess as a poet.
One use of repetition is with the word "hook," which appears twice in line three, suggesting that the body of the hawk is a kind of symmetrical arrangement of hooks (head and feet). The poem returns to the idea of the hooked foot in the third stanza, in which the hawk's "feet" are "locked" in the "bark"; the image of the foot (not, interestingly, the more appropriate "talons") returns over and over, a symbol of the hawk's evolved nature and his absolute dominance.
Hughes's use of repetitive sounds, especially the hard k sounds alternating with the softer fricative f sounds, as in the third stanza's use of "locked" and "bark" as contrasted with the "foot" and "feather" two lines later suggests the double nature of the hawk's world, in which the bird is both remote and passively watching and immediately present ("For the one path of my flight is direct / Through the bones of the living").
Finally, Hughes's syntax in the poem is remarkably obtuse. The complex and convoluted structure of his sentences and the reading rhythm they create suggest the power and vigilance of the hawk and his sudden action. Take, for instance, the sentence "No arguments assert my right: / The sun is behind me." First, the sentence is split between two stanzas, so even though it is one sentence, we can read the beginning of the sentence as the end of one stanza and the end of the sentence as the beginning of the next, a move which encourages the reader to not think of the two parts as connected at all. The colon suggests equivalence or cause and effect between the two statements, as if flying out of the sun is all the argument the hawk needs.
The hawk's elemental sense of power ("I am going to keep things like this") is also, in my view, an expression of Hughes's sense of poetic power. While it could be argued that the hawk's sense of independence is a kind of self-delusion, in a way, Hughes's handling of language in this poem is his way of asserting that "no arguments" are needed to assert his hawk-like authority.