Through examining hymns of exultation, we can attain a sense of how an individual perceives him or herself. So, by looking at one of Assurbanipal’s prayer to Ishtar of Nineveh and Arbela, we can get a sense of how Assurbanipal perceived himself, or at least how he wants others to perceive him.
The prayer may be summarized as follows: First, the speaker extols Ishtar of Nineveh and Ishtar of Arbela, who are to be understood as two distinct deities (lines 1-7). Subsequently, the speaker identifies himself as Assurbanipal and describes how the goddesses supported and currently support him, from birth to his current success as king of Assyria (lines 8-44).
Now, this hymn contains a plethora of rich imagery which could help us to understand how Assurbanipal perceives himself. I will focus on one aspect, though. In particular, I want to focus on how Assurbanipal represents himself as having been raised by a divine goddess. I suggest that this self-representation is conceptually related to how Marduk, a mighty warrior deity, is represented in the myth titled The Babylonian Creation Epic (Akk. Enūma eliš). First, I will discuss the relevant sections of each text independently. Second, I will point to the particular similarities in terms of the motifs and imagery employed.
In Assurbanipal’s hymn, Assurbanipal represents himself as having been raised by the goddesses:
I (am) Assurbanipal, their hearts’ desire,
Great seed of Baltil, [bo]rn at Nineveh,
Formed in the [Emashmash], and the Egashankalamma,
Whose kingship they [sum]moned(?) from the [crown prince’s] palace
They have [ordered] with their holy command that my throne long endure.
I knew neither human father nor mother, I grew up on my goddesses’ knees,
The great gods have guides me like an infant…
They made my physique splendid, they made mighty my strength,
They exalted my name over any other ruler’s. 
What stands out in these lines is how the goddesses themselves summoned Assurbanipal, ordering his kingship. Then, in describing his upbringing, he likens himself to an individual without human parents, an extraordinary experience for a human being. Subsequently, these gods are attributed with having made his strength mighty and physique splendid. In other words, he perceives himself as having been made into the ideal human and king, both caused by the goddesses.
Another text, commonly called The Babylonian Creation Epic, contains a similar description of a Marduk, a central deity in Mesopotamia who was known for defeating the mythological dragon of Chaos named Tiamat. Importantly, The Babylonian Creation Epic is a mythological narrative about Marduk’s ascent to primacy within the divine pantheon. So, the beginning of the narrative takes great care to represent Marduk as a mighty, fearsome deity. When Marduk is born, the narrative describes how he was raised:
He sucked the breasts of goddesses,
A nurse reared him and filled him with terror.
His figure was well developed, the glance of his eyes was dazzling,
His growth was manly, he was mighty from the beginning. 
Here, Marduk is represented as having been raised by goddesses. Unlike Assurbanipal, though, the goddesses are not attributed with making Marduk mighty; rather, he just was so from the beginning. Instead, Anu, father of Marduk, is attributed with rendering Marduk perfect (lines 91-92).
When placed side-by-side, an important theme emerges: the mighty-warrior-to-be who was raised by goddesses. Although framed in distinct ways, both Marduk and Assurbanipal are represented as being raised by goddesses. And while I don’t have evidence to suggest that Assurbanipal expressed himself as he did in order to compare himself to Marduk, it is plausible that Assurbanipal used the theme with full awareness that this was how mighty divinities were sometimes represented within other texts .
Thus, we return to the initial question: how did Assurbanipal want others to perceive him? On the basis of the previous discussion, I suggest that Assurbanipal wanted to be perceived as one who was intimately connected to the divine realm. By representing himself as having been raised by goddesses, he successfully integrates himself into the divine realm. Additionally, by emphasizing his perfect physique and might as originating from the goddesses, he is represented as an extraordinary human. He is, to a certain degree, representing himself as a superhuman, being part man and part divine.
 Benjamin Foster, Before the Muses (Bethesda: CDL Press, 2005), p. 820.
 W. G. Lambert, Babylonian Creation Myths (Indiana: Eisenbrauns, 2013), p. 55, lines 85-88.
 This gains support from the fact that The Babylonian Creation Myth was so well-known during the 7th century BCE, itself being part of a cult ritual. For other references to the role of two goddesses in raising Assurbanipal, see Barbara Nevling Porter, “Ishtar of Nineveh and Her Collaborator, Ishtar of Arbela, in the Reign of Assurbanipal,” in Iraq vol. 66, Papers of the 49th Recontre Assyriologique Internationale, Part One (2004), pp. 41-44. She notes two texts aside from the text we are examining. In both texts, goddesses are attributed to having suckled the royal baby Assurbanipal. Moreover, a commentator on Enūma eliš suggests that the “nurse who raised Marduk” was actually Ishtar of Nineveh, one of the two Ishtar-figures referenced at the beginning of the hymn. Although this isn’t proof for interpreting The Babylonian Creation Myth, it does support the general thinking that Assurbanipal’s being raised by Ishtar of Nineveh is conceptually similar to Marduk’s being nursed by goddesses. See Eckart Frahm and Enrique Jimenez, “Myth, Ritual, and Interpretation: The Commentary on Enūma eliš I–VII and a Commentary on Elamite Month Names,” in Hebrew Bible and Ancient Israel 3, Vol. 4 (2015), p. 301.