Her fighting style? Well, she has both a shovel attack (melee) and a grappling hook(ranged). The shovel is very similar to Rapunzel's melee frying pan while the grappling hook is like Mrs. Incredible's powers.
I usually just use her shovel for combat. Her grappling hook isn't the greatest attack, since it just pulls enemies to her. After pulling an enemy closer, she can beat 'em up with her shovel. I prefer to use the grappling hook as , well, a grappling hook. It's great for platforming, since it pulls Anna to whatever she hits with it.
You've probably heard this all a million times before, but it's what I know about Anna's fighting. You can watch her fight at 1:40 in this video:
https://www.youtube.com/watch?v=V_TlGqiH_Hw