Her forward tilt is a bit odd to me. That move, as laughably weak as it was, is pretty slow for a tilt. Obviously slow powerful tilts CAN exist, but it seems like an attack that would be much better used in a Smash attack. Just personal opinion though, I guess.
I have no reference for what that dash attack is referencing, but assuming it's anything like her sliding pose from the HGH autoscrollers I kinda love it. It's silly, and that fits her really well.
Her Fair/Bair/Uair are... eh? For one, a spinning move like that doesn't seem very forward to me, especially if it hits in both directions. I used that for her up air, because I feel like it's a lot more fitting. A move similar to Samus's up air, except with her hair instead of turning upside down to use her feet. Using the flamethrower for back-air is dubious at best. I might just not be seeing it right in my mind, but projectile aerials are something I feel like you should typically avoid unless it's for a character who is specifically projectile oriented, like Mega Man or Mii Gunner. Up air seems decent enough, other than not feeling like it's based on much of anything. Without trying to sound TOO biased, I made Fair her whip attack as well, so you could more easily approach with it. Mega Man has a different Fair, but he doesn't exactly need pellets on his Fair either. I dunno.
Her down-air and down throw should be switched, IMO. The drill kick works fine as a down-air, but using her scimitar like that for a throw just seems... odd. In order to do that attack, she'd need both hands, and since it's not a tether grab with her hair, the physicality of it doesn't make much sense. Using the drill kick as a down throw seems a lot more realistic to me.
Her other throws don't have the same problem, since they can easily be one-handed sword slashes, but at the same time they just don't feel particlarly Shantae-like to me. Shantae is not a swordfighter at all, she only uses a sword occasionally for very unskilled moves. Having her do swordfighting techniques like this just doesn't feel in-character to me.
The way you did her specific transformations is almost exactly the same as I did, except with one difference. Giving harpy a projectile, I think, is way too strong. Harpy is already going to be based around moving around and controlling the air, so giving her a projectile, no matter how crappy it is, is probably a bad idea. I suppose it could be balanced, but I think it's better off sacrificing the "canon" of her harpy form to keep it more reasonable in Smash context.
The other three transformations are pretty much exactly how I did them aside from the specifics. No complaints here obviously

The only thing I could say about them is that you put Elephant as the down transformation and Spider as back, which makes maybe slightly more sense intuitively, but is less accurate to HGH. In HGH, Elephant is the back transformation on page 1, and Spider is the down transformation on page 2. Not a huge deal, really.
As I mentioned before, I think giving her a projectile, especially one that goes in three directions like you have it, is too strong for the rest of her kit. Spider having a good projectile is fine since it's locked behind her transforming, but having a projectile with easy access to it at all times is just downright busted for this kind of character. Even if the way you set up her normals is slightly less based around disjoints with her hair, combining a character with good speed and range with a good projectile can end up overpowered very easily. (Imagine if Mario had a disjointed move like Shantae's hair whip, on top of his already good neutral game with his speed/projectile. It'd be busted as hell.)
I like the up special, even if it is mostly original in function. It's cute.
If pike ball can't be thrown, I think giving it 3 projectiles and making it super pike ball would be better the way you're describing it. If she can't do anything while it's out like Mega Man's leaf shield, then only having one of them is just gonna make no one use the move ever. Unless it did a ton of damage or something, but that'd be a little out of place IMO.