"Let the eagle soar" (speculating with mythemes)

Tap dancing Roman bronze eagle, 100-200CE (Gettyvilla Gallery 209)

Zeus’ lightning and thunderbolt holding eagle were no different from Zeus himself, and symbolised his power, majesty, and dominance. He would send his eagle down to strike those defying him or those showing excessive pride (hubris). Imperialist rulers would use Zeus’ attribute to symbolise their own will to power, power, majesty, and dominance, such as the Achaemenids, Alexander the Great and the Roman emperors. 

Zeus/Jupiter, his lightning (vajra). Coin, Epirus 234BC

However widespread their empire, the large-winged eagle would find and strike the rebellious ones. Nothing would escape his sharp eyes.

Emblem of the Roman empire, Jupiter's eagle and lightning

Zeus, eagle and Prometheus (c. 560 BC, Louvre), thunderbolt at the bottom?

“Ready-witted Prometheus he [Zeus] bound with inextricable bonds, cruel chains, and drove a shaft through his middle, and set on him a long-winged eagle, which used to eat his immortal liver; but by night the liver grew as much again everyway as the long-winged bird devoured in the whole day.” Hesiod, Theogony 507 ff (trans. Evelyn-White) (Greek epic C8th or C7th B.C.)

Heracles frees Prometheus from "the Caucasian eagle" (theoi)

Later, the demigod Heracles, Zeus’ son, probably with the approval of Zeus, made an end to Prometheus’ suffering by slaying the eagle. Heracles also slayed the Lernaean Hydra, a multi-headed water serpent. The latter theme and associated subthemes have been shared in Indo-european cultures.

"[Zeus] drove a shaft through his middle" (Hesiod)
Here a thunderbolt nail or peg (phur-ba, tsakli)

Three types of vajras (site)

The thunderbolt (vajra) bearing Indian god of storms and war Indra defeated the monstrous serpent-like asura Vritra, In another Indra myth, Garuda appears, as Amṛtaharana, the "stealer of amṛta", not the stealer of fire this time…

“The Vedas, composed in approximately the second millennium B.C.E., provide the earliest reference to Garuda, though by the name of Śyena (Sanskrit for "eagle"). In Rg Veda (1700–1100 B.C.E.), this mighty eagle fetches soma, the intoxicating ritual elixir, from either a crag in a rock or from heaven itself. Both the Mahabharata (c. 400 B.C.E. - 400 C.E.) and the Puranas, which came into existence much later, have Garuda performing similar mythological tasks, suggesting that Śyena and Garuda are one and the same figure.” New World Encyclopedia

The "high crags of the Kaukasos (Caucasus)" (Apollonius Rhodius, Argonautica 2) ?

Marduk fighting Tiamat (Assyrian cylinder seal, ca. 800-750 BCE)

In the Garuda purāṇa (9-11th century) we are told a myth that reminds the one of Marduk destroying his grand-mother Tiamat (saltwater) in a titanic battle, found in the Poem of Creation (Enūma eliš), written during the reign of Nebuchadnezzar I (1125-1104 BCE). The Garuda purāṇa:

“One day, Vinata [Garuda’s mother] entered into and lost a foolish bet with her sister Kadru, mother of serpents. As a condition of her defeat, she became her sister's slave. Resolving to release his mother from her newfound state of bondage, Garuda approached Kadru and her serpents and asked them what it would take to emancipate his mother. Kadru decreed that Garuda would have to bring them the elixir of immortality, also called amrita. This was a tall order indeed, considering that the amrita was at that time in the possession of the gods in heaven. Indra, the mighty king of the gods, guarded it jealously. In order to protect the elixir, the gods ringed it with a massive fire that covered the sky. They had also blocked the way to the elixir with a fierce mechanical contraption of sharp rotating blades. Lastly, they had stationed two gigantic poisonous snakes next to the elixir as deadly guardians.

Undaunted, Garuda hastened toward the abode of the gods, intent upon robbing them of their treasure. Well-aware of his powerful design, the gods met him in full battle-array. Garuda, however, defeated the entire host and scattered them in all directions. Taking the water of many rivers into his mouth, he extinguished the protective fire the gods had thrown up. Reducing his size, he crept past the rotating blades of their murderous machine. And finally, he eluded the two gigantic serpents they had posted as guards: even the quickest glance of these snakes was deadly, and so Garuda subdued them by blowing dust in their eyes. Taking the elixir into his mouth without swallowing it, he launched again into the air and toward the heavens. En route, he encountered Vishnu, who was impressed with Garuda's might. Rather than fighting the bird, Vishnu decided to reward him with a boon: the gift of immortality, even without drinking from the elixir. In return, Garuda gratefully requested that he become Vishnu's mount. Flying onward, Garuda encountered Indra. The king of the gods hit Garuda with his thunderbolt, but Garuda was virtually unscathed by the blow, losing but a single feather. Fully aware of Garuda's power, Indra called for a truce with Garuda, and so another exchange of pacts was undertaken: Garuda promised that once he had delivered the elixir, thus fulfilling the request of the serpents, he would make it possible for Indra to regain possession of the elixir and to take it back to the gods. Indra in turn gave permission to Garuda to have the nagas as food.” (New World Encyclopedia)

Garuda statue, Phnom Penh, 10th century (ANI)

Several older myths of gigantic powers seem mixed here. One could speculate Garuda is presented here certainly not as a creator of heaven and earth, but as one that puts an end to chaos and restores order, like Marduk who uses a net to entrap Tiamat (saltwater) and to split her in half, using her upper half to create the heavens (heavenly waters), and the lower half to create the earth. At the same time there is the soma (amṛta) theme. In the case of Garuda the amṛta was ingested (without swallowing) and spit out again towards heaven in order to restore the balance. After putting an end to the chaos (of mingled heavenly and earthly waters, flood), Garuda remained at the service of Viṣṇu (and no doubt Indra), as the heavenly creature capable to use and dominate the fluid element (nāgaloka), and everything associated to it.

The universal dimensions of Zeus' eagle and Garuda can be found back in narratives of giant birds such as Peng and Roc. 

The 9-11th century Garuda Purāṇa contains many elements Tibetan Buddhist traditions may have well been interested in, specifically the details about the ghost world (pretaloka, pitṛloka) and the funeral rites.

“2.22.7 Sinful persons meet with death at the hands of candalas, infuriated brahmanas, serpents, animals with curved teeth or in watery graves or struck by lightning.

2.22.8-13 Those who meet with foul death such as committing suicide by hanging from a tree, by poison or weapon, those who die of cholera, those who are burnt to death alive, those who die of foul and loathsome diseases or at the hands of robbers, those who are not cremated duly after death, those who do not follow sacred rites and conduct, those who do not perform Vṛṣotsarga[1] and monthly pinda rites, those who allow śūdras to bring sacrificial grass, twigs and other articles of homa, those who fall from mountains and die, those who die when walls collapse, those who are defiled by women in their menses, those who die in the firmament and those who are forgetful of Visnu, those who continue to associate with persons defiled due to births or death, those who die of dog-biting or meet with death in a foul manner, become ghosts and roam over the earth."

A last anecdote regarding Zeus’ eagle (Aetos)

“There is a story of Zeus’s eagle which should be told at this point. There was a boy named Aetos, eagle, who was born of the earth, like the Idaean Daktylos, Kelmis, of whom I have already spoken, and who, like the last-named and the above-mentioned Aigipan, was supposed to have been a playmate of the child Zeus. He was beautiful, and Hera turned him into an eagle because she suspected that Zeus loved him.” The Gods of the Greeks[2].

This boy is also known as the youth Ganymede, that Zeus, having taken on the form of an eagle, transported to Mount Olympus. The eagle was placed among the stars as the constellation Aquila alongside Lyra.

Aquila constellation

Vajrakila (rdo rje phur ba), HA21299

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[1] “Setting at liberty of a male and female calf (as a rite in funeral solemnities) : also of a bull (as a religious act generally)”. Wisdom Lib

[2] Kerenyi, Karl (1951). The Gods of the Greeks. London: Thames and Hudson. p. 95. Quoted from Aeneis, Virgilius, I.394.