Is there a specific arc for Sinon in the anime? I'm rewatching the whole SAO series and I go to the manga whenever I want to clear things up for the show but I thought about something. 

In the Aincrad novels, there are specific chronological Arcs for:


  Silica, Lizbeth, Yui, Sachi


But in the second season, we see Sinon, a "main?" character. But isn't there a specific Arc for her? or some more backstory than what we see in the Anime? 


   The fact that she gets scared of guns but in-game she isn't, and her past at the bank.


I couldn't find any Arcs for the characters of the second season so if there are where can I find them or what are they called?
The whole Phantom Bullet arc is Sinon's arc, in the same way the Fairy Dance is mostly Leafa's arc, for the most part. Neither character has another side-story outside of these arcs, seeing as most of their past is expanded within them.

In the Light Novels, this is Volumes 5 and 6. Most of what you want to know about Shino/Sinon will be in those two volumes.