Well the word of the week is banding, and its whats giving your AA a blurred look instead of smoothing like it should.
You want to keep the sharpness that pixelart gives you, don't be afraid to cut into the lines but try keep it as thin as possible as your trying to trick the eye into thinking its smoother than it is.
I'd try AA a single line to the side of this for practice just a small curved bit of linework, but I've made an edit of places here and there anyways to illustrate how I'd go about this.