sort posts alphabetically plugin

I was hoping to find a plugin which would enable my posts to be automatically sorted into alphabetical order, not only that but the A posts, would need to display in the A section alphabetically, the B posts in the B section alphabetically, the C posts……….

Currently my website has a section for the A B C D….. and shortlinks at the top of the page to skip to the letter which is clicked.

I figured displaying the posts could work very similar to the archives page of the website and just sort this in alphabetical, but that still wouldnt solve the issue of putting the posts in the particular letter sections. I have already categorized the posts I need.

http://thingsiveplayed.com/pc/free-to-play/ <– this is what all sections will look like, and this is where the posts need to be displayed.