Board Thread:Questions and Answers/@comment-25908228-20141222101442/@comment-4567891-20151004210720

They've already had a duel in the canon doujinshis where they had a disagreement over using NPCs as fodder. What followed was a battle that went on for 20 minutes straight with neither gaining an advantage until Kirito had to use a Martial Arts Skill to take her off guard in order to beat her. And in SAO Progressive Volume 1, Kirito outright admitted that her attack speed with a rapier was so swift that he couldn't keep track of her sword at all. In the same volume, when they had a contest between them about who could kill 50 enemy bees, he realized that he was lagging behind her on kills, so he again had to resort to using Martial Arts Skill mixed with his Sword Skills to keep pace with her.

So, in at least two occurances, Kirito has had to fall back on tricks outside of his swordsmanship to beat Asuna.