I do not claim to be an expert on Greek mythology, but I've always been fascinated. This is giving me a chance to research and learn more about the aspects of the mythology that effect Wonder Woman.
The first mythological aspect that we see is Apollo himself. Though it is never explicitly stated in the issue that he is Apollo, the dialogue in this image ("I'm the Sun of a King"), heavily implies it, with Sun being a play on words (Apollo is the son of Zeus and the Sun God). [Note: There was a character design image released by DC Comics that clearly states that this is Apollo.]
Apollo is the son of Zeus and Leto. His twin sister is Artemis, the Goddess of the Hunt. "Apollo has been variously recognized as a god of light and the sun, truth and prophecy, medicine, healing, plague, music, poetry, arts, archery, and more." [Wikipedia]
This is a very interesting interpretation of Apollo. He starts out with dark skin and hair, almost like molten rock. As the sun starts to rise throughout the issue, he gets brighter until this:
Next we see someone (seemingly female) cloaked in peacock feathers. We never get a look at this person beyond an arm, a leg, and a silhouette. The peacock has long been associated with Hera, queen of the Gods [*]. She is frequently shown as being very jealous of her husband Zeus' many lovers. If she knows that Zola is pregnant with Zeus' child (as revealed at the end of issue 01), it makes sense that Hera (or perhaps an agent of Hera) would attempt to kill Zola.
Next we see Hermes, the messenger of the Gods. In George Perez's reboot of Wonder Woman in 1987, Hermes is the God who gifted Diana with speed and flight. Here we see him with winged bird feet and a helmet similar to the one he wore during George Perez's run [**]. No caduceus in sight.
Centaurs! Body of a horse with the torso and head of a human. There are two different origins for centaurs, both of which have connections to happenings in this issue. In one, centaurs were born of Ixion (son of Ares) and Nephele (a cloud nymph in the form of Hera [***]). In the other, all centaurs are descended from Centaurus. Centaurus is either the child of Ixion and Nephele, or the child of Apollo with Stilbe (a water nymph and daughter of River God Peneus). Whether connected through Apollo or Hera (or even not at all), centaurs play a heavy role in Greek mythology. It makes sense that Wonder Woman would come across them.
Finally, we have these three. Though these three start out as regular human women, they seem to be Oracles of some kind. It is possible they were nothing more than regular oracles (perhaps even imbued with the power of Apollo). However, the fact that there are three of them and they speak in turn could be a reference to the Moirae, the spinners of fate. The women could have been channeling the Moirae. It is unclear exactly who they were and why they could foretell the future.
That's all for this issue! Come back next month when we examine mythological aspects of issue two!
[*] The story of Hera's association with the peacocks revolves around Zeus' affair with Io.
[**] George Perez's Hermes can be seen here. This image was from Wonder Woman (v2) issue 07.
[***] Nephele was made by Zeus in the image of Hera to test Ixion's integrity. Ixion has shown lust for Hera. He failed Zeus' test and mated with Nephele (whom he believed to be Hera). And thus, the centaurs were born.