My impression was the Nike can sense the rapid disruptions in the wind from things like arrows and crossbow bolts. She already got shot once protecting Livi from assassins. It wasn't clear whether it was the glint of the arrow tip or the wooshing air of the arrow getting fired. It seemed like both. She noticed the arrow glint, but only moved to protect Livi after it was fired. She couldn't know what the glinting she saw was, but once it was fired she knew where it was going.

@shinta:
How much shoujo do you read? You'd know that the love triangles in shoujo never matter for very long. It's not like shonen or seinen where the triangles are never resolved. Nike will overwhelm this other girl with her awesomeness in short order. Then this new girl will be forced to swear her eternal allegiance to Nike.