personality
First and foremost: Amaterasu is the goddess of the sun. She is known as the origin of good and called a mother to all. So she can display a bit overprotectiveness of others since the people of Nippon are, technically, her children and it is a mother’s job to protect her children! As well as reprimand them when they do thing. So, at times, this reprimanding comes in the form of tough love. If by tough love that means “there is a child acting like a cry baby, let’s give him (or her) a headbutt to make them stop.” Surprisingly? It works. Especially when Issun gives the kid a bit of a talking to.
Despite being a goddess, however, most people just take her for a simple dog due to the fact that they are unable to see her markings (and even then, those who can see them don't really make comments on them). So they treat her as such, usually making comments about things because they think that she doesn’t understand them. Mr. Orange had gone so far as to say that while Amaterasu resembled Shiranui, she didn’t look quite as smart. Those sorts of comments are enough to irritate her, even if people may just be stating facts.
That fact may be just a little true. As knowledgeable and smart as Amaterasu is when it comes to certain things, there are also others that she can be confused by or just be relatively ignorant to. After Orochi’s defeat, Kamiki village had a celebration and Kushi and Susano were no where to be seen; when Amaterasu went to find them, and spoke to both of them, Issun made the remark that she doesn’t quite get it and that the two of them wanted to be alone.
She’s also got a bit of a competitive and playful spirit and is always willing to challenge someone to a race. It means that she gets to have some fun while showing off her speed. When the race is finally won - or, really, whenever she does anything that could warrant a bit of an ego boost - she can get rather huffy and overly proud of herself. And if that winning gets her some sort of prize, may it be material or a headpat, then she has achieved what she set out to do. Especially the headpatting.
After all, Amaterasu loves receiving (and giving) affection. While some people may offer the affection without needing a motivator to do so, Amaterasu can use her Bloom technique on an unsuspecting person and cause them to come and shower her with either headpats, being petted, or a hug of some sort. She rather enjoys abusing said technique for those purposes alone.
However, as driven as Amaterasu is to defeat the evil that plagues Nippon and save the land, she has a tendency to be slightly aloof, stubborn, and would probably end up lazing around if Issun was not with her. (The latter bit is something that he makes mention of in Okamiden, when speaking to Chibi.) She’s easily made bored if a person is going on a rather long tirade or speech or explanation; she does this shortly after Sakuya calls upon her for help, when she first meets with Waka after 100 years, and while the Spider Queen takes to ranting a bit. She may also take to napping even when there are other pressing matters at hand.
But when it comes to decision making and whether or not to just go head in with a battle against a boss? Amaterasu the type who would much rather leap into something before thinking about it, of which Issun has become quite used to and “Leap before you think!” has become their motto and way to live by.
But she’s got a good head on her shoulders and she does her best to help the people of Nippon in any way that she can - whether it be through using her brush techniques or playing a digging game with them. It means that she can help restore their faith, little by little. One person at a time.