The Shapeshifter's/Himawari's goal seems mostly to survive/exist.
Long Maya implied that she was scared of revealing the name of Ayane's lost baby as it'd affect her future:
And a Narrator, which may be her, more or less said "I'm helping cause I want to exist" in the 'World of Lines' Chapter 3 Main Event:
So, in theory, she's doing all that she can to ensure a possible future comes to past, so that she can safely exist. Whether or not she's from a future or is only allowed to exist if that future remains possible for her to play a part in, I'm not sure.
She also seems to value Sensei, and Ayane, possibly Sana, and shows up a few times only if you're fucking Ami and Sara, so they presumably play a part in things.
The Shapeshifter was also shown with Ami clones(?):
And apparently has coworkers, besides the Mayas, like Shiori, who may be Nodoka's evil twin:
Albeit, Shiori may also just be a Shapeshifter, who looked like Nodoka to Nodoka at one point or something. (Or it's just a coincidence which I somewhat doubt)
Overall: It's not clear, but I'm leaning towards Survival being her main motivation.
The happiness and safety of Sensei and Ayane, are probably motives as well, and making the world a better place is probably another, if this was her, which I think was implied: