I wonder if it's possible to beat the game only using the polar star 
I don't think you can get the best ending without the Spur, can you?
I got to the last save point before the consecutive final boss fights (other than ballos of course) and took a break. A long break. Still haven't gone to try and beat them, especially now that I've found out that I got Cave Story+ as a game that was added on a Humble Bundle.