Today, we have a question more about the game's mechanics than the mythology surrounding it: Any chance of telling us how shapeshifting works in the game? However, this is really as much of a question about shapeshifting and what it really is across different world myths as it is one about exactly what the game does with them, so it'll be a little of column A and a little of column B!
This is actually a wide-angle kind of question without a single answer, because shapeshifting is a very complicated idea and appears in a lot of different forms and for a lot of different reasons across different cultures' tales. Shapeshifting doesn't mean the same thing to every culture, and there are often different kinds of shapeshifting within the same culture as well, each with various symbolic value or used by different kinds of characters for sometimes very disparate purposes. Asking about shapeshifting in general is a little bit like asking how the game handles "nature" or "fighting"; there are a lot of ways it can be answered, depending on your definitions and what you're actually looking to do.
The idea of changing oneself is at the heart of most heroic stories, although not always in a blatantly obvious manner; most Heroes must in some way change or become something new as they experience their adventures, or else face the danger of failure if they cannot adapt or find ways to become what is required of them. Some mythological characters literally transform into a completely new being in order to do what they need to do - for example, Vishnu, who must transform himself into the giant turtle Kurma in order to support the gods' quest to churn the Ocean of Milk, or the tale in which Loki and Heimdall transform into seals in order to have a giant wrestling match in the sea. Other times, the Hero must change something in their personality in order to succeed, such as when Herakles must perform various gruelling tasks to atone for his sins and become a hero again. Still other times, shapeshifting is a means to an end, a way for a character to represent themselves as one thing while actually being another; this is the case when Isis disguises herself in order to speak at her son's hearing, thus avoiding the rulings against her, or when Zeus impersonates Alkmene's husband in order to have his way with her without her realizing that she is not being faithful or disguises himself as the swan that impregnates Leda with the beautiful Helen of Troy.
Because shapeshifting means so many things and is done in so many ways and for so many purposes, it doesn't look the same or occur the same across all (or even most) myths. Some of the basic mythic shapeshifting archetypes you might see in mythology include:
Disguise Transformation. This kind of shapeshifting is used to hide the Hero's true form, usually in order to either escape danger or go undercover to learn information or perform unnoticed shenanigans. Sometimes this involves putting on an impenetrable disguise, which is popular in Norse myth - for example, Odin transforms himself into an old woman in order to travel the world and perform witchcraft without being noticed. Sometimes it involves changing oneself to misrepresent the Hero's intentions, background or abilities, anywhere from as complicatedly as the Great and Powerful Oz pretending to be a giant dangerous head to as simply as the Biblical hero Ehud pretending to be right-handed in order to pull off some sweet left-handed assassination without anyone stopping him.
In Hero's Journey, this is handled largely right where you would expect it to be: in the Disguise Talent, which is rolled for normal disguise endeavors like throwing on a beard and cloak so your friends don't notice you in the corner. It also governs the portion of the Web of Fate in which the Blessings having to do with this kind of misrepresentation are located - powers that allow Heroes to change the details of their physical appearance and confuse others into thinking they're someone or something other than what they are.
Personal Transformation. Personal transformation, on the other hand, is about the Hero literally becoming something new. In most myths, this means that the Hero needs to become something they're not to succeed, or that there is an alternative source of power that they can only reach into by changing themselves. Examples of this kind of shapeshifting include folkloric witches who transform into animals in order to take on their powers or Heroes like Toyotama-Hime, who while originally the scaly daughter of the dragon-king Ryujin turns herself into a human form in order to marry the humanoid divinity Hoori. Often in mythology, you see this kind of transformation in reverse, coming from non-human and non-Hero sources who become human in order to do things they otherwise couldn't, like the Japanese kitsune that become human in order to enact mischief in mortal courts.
Exactly what powers a Hero might use for this kind of shapeshifting is debatable, since a great deal of its execution depends on the intent of the person doing it. Disguise Blessings are still an option, especially if, like the aforementioned kitsune, the goal is to fly under the radar or try to pass oneself off as something that you aren't. On the other hand, Heroes who truly want to change who and what they are may need to invest in Blessings that have to do with the specific thing they want to become, by nature stepping outside the zone of those human-like Disguise powers and intentions. This kind of shapeshifting is often intended to be permanent - it's not a feature of general trickery, but a way of allowing a Hero to intentionally become something entirely new.
Aspect Shifting. This kind of shapeshifting involves a Hero swapping between different aspects or versions of themself, all of which are in fact true expressions of the Hero but which may appear in order to represent different ideas or grant them access to different powers. This happens very frequently in Hindu mythology, where the idea of the Avatara, an incarnation of a deity on earth as a new Hero, is an example of this kind of shapeshifting and allows them to perform actions or become symbols of ideas that normally don't apply to them; and similarly, Hindu gods also often take on different forms appropriate to what they need to do at the time, such as Shiva becoming Bhairava, the Annihilator, when it's important that he appear as the ultimate manifestation of destruction.
Aspect shifting occurs in a lot of different cultures (another good example are the nahualli of Mexican mythology, which can appear as alternate aspects of Heroes or which Heroes may sometimes transform themselves into without actually becoming something different). While there are powers scattered around HJ that can be used this way, and of course Heroes can use any of the other shapeshifting powers to encourage this kind of image of themselves, most of this is handled by powers in the Devotional Domain, which is in charge of ideas specific to a Hero's pantheon and the religion of their patron.
Self-Denial. Self-denying transformations are rare but critically important to the myths in which they happen; they involve a Hero choosing to not become something new but to give up their identity and embody something that is not themself, in essence sacrificing something (temporarily or permanently) to become part of something else. This is common in Heroes and deities that are associated strongly with nature, such as the Nigerian river goddesses Yemanja, Oya and Oshun, all of whom transform themselves literally into rivers and become one with features of the landscape rather than independent actors on their own, or in tales about the indigenous deities of the Inuit, who often embody natural forces like wind or earth more often than they appear as discrete beings in their own rights. Sometimes this means that the element speaks through the Hero, making them a mouthpiece, while other times they simply disappear into it, and possibly re-emerge later changed or with new knowledge thanks to the experience.
This can also occasionally happen in reverse, with the landscape or some other primordial force coming together to personify itself (usually in response to some upheaval or tragedy), but this doesn't happen as often, especially spontaneously as opposed to involuntarily (see below). Heroes who want to perform self-sacrificing shapeshifting are definitely filling more of a niche role that isn't common to all myths, but it's still a possibility; they need to look to the areas of power associated with the thing they want to become part of, so those wanting to become one with the waters, for example, are best served seeking out Blessings in the Water Sphere of the Elemental Domain.
Involuntary Shapeshifting. This is exactly what it sounds like - shapeshifting that happens whether the Hero wants it to or not (usually, not). The most classic example of this for most people is probably the modern idea of the werewolf, which has to transform into a beast at the full moon whether it wants to or not, but the idea pops up all over mythology and folklore in various nooks and crannies. Usually, this kind of transformation signifies something in the Hero's nature that cannot be hidden or resisted on more than a temporary basis, and which must appear when it is time for it to do so whether or not they would prefer to avoid it. Often, this is the result of a magical item that affects its owner, but it can also be innate - for example, the selkies of Celtic myth turn into humans when they remove their skins, and are unable to return to their former shape unless it is returned to them.
Involuntary shapeshifting is, well, involuntary, so it's unlikely that it's something that Heroes will be intentionally performing on themselves. However, it's entirely possible to end up with an involuntary shapeshifting condition - for example, a Hero could become a werewolf or other kind of shapeshifter, or gain a magical item that messes with their shape - and therefore have it added to the story by an outside force. Heroes could also begin with special conditions from their patrons, although there aren't a ton of gods out there who would probably find giving their Heroes an involuntary transformation reflex very useful in the grand scheme of things.
Inflicted Shapeshifting. And, finally, there's shapeshifting that is directly inflicted on someone by the powers that be, usually as a curse, punishment or assault on their way of life. This is a classic fairy-tale device - both the Princess and the Frog and Beauty and the Beast, for example, hinge on someone inflicting a shape-change on a Hero who must then figure out how to un-inflict themselves (preferably as quickly as possible). In Irish mythology, the children of Lir are transformed into swans by the power of the jealous goddess Aoife, and Greek mythology is rife with stories in which various deities turn some hapless mortal into a plant, animal, constellation or other inhuman form in order to punish them or occasionally save them from some pursuer or danger.
This is really a method of dropping any of the previous kinds of shapeshifting on the head of someone who wasn't planning on or capable of doing it themself; for example, some werewolves are considered to be cursed by an evil power, thus having their unstable condition inflicted on them, and some Heroes who go through transformational changes must find a magician, deity or powerful ally to help them do so, achieving a new state they couldn't alone. Heroes who want to inflict unauthorized shapechanges on others will most likely find themselves investing in powers in the Spiritual Domain, where control over living things and their destinies is the order of the day.
There are a lot of other specifics and quirks to the idea of shapeshifting, but we'd be here all day if we tried to cover all of them at once. The basics are above, but keep in mind that there are myriad variations on them that you might see in mythology; transformations involving only a single part or feature of a Hero, for example, or situations in which the Hero is not truly shapeshifting but only seems to be, also add to the overall picture of the vast possibilities for Heroes and change across the stories of the world.