A 2012 Macbook Air can run Sierra.
<MacOS Sierra - Technical Specifications>
MacBook Air (Late 2010 or newer)
Notice the "or newer".
As I said, I just upgraded a Macbook Air older than yours to Sierra. There should be no problems upgrading yours.
I would try doing the upgrade from Safe mode
Try booting into Safe mode
<http://support.apple.com/kb/ht1564>
This will not load any 3rd party additions, it will load some more conservative Apple drivers (may cause screen flicker), and it will clear some kernel caches (a cache is saved data in a form that can speed up a program, but is totally redundant to the original source, and thus can be safely cleared). Booting into Safe mode is just an experiment, but can often times eliminate any 3rd party interference, or a cached item out-of-sync with the world.