A brush edge only gets so hard in Photoshop. Once you push the hardness to 100%, there's no way to further remove any anti-alising. You can try working at a high PPI and then reducing, but that can be guesswork more than anything.
Vector layers in Photoshop can often have a bit less anti-aliasing than brushes. You might try using the vector tools rather than brushes.
I'd suggest that the original sample you've posted may have been created originally outside of Photoshop.
Vector artwork.. placed as a Smart Object into Photoshop, then rasterized (if necessary) will have less anti-aliasing than painting directly in Photoshop.
My guess.. that's how the original was created... even the artwork itself suggests it would be easier to create in a vector application - at least the keyline.
Zoomed in to just before the pixel grid shows (300ppi file)....