I have a character whose Blade Song is interpreted as less magical than a sort of meditative focus which allows him to create a visual overlay in his mind, essentially projecting an Augmented Reality display in his field of vision (like iron man). He sees the circle of his own fighting space, those of other creature he can see, and all the tangent lines that connect and intersect within those, as well as the concentric circles of range, sound, normal focus, etc.
So, when he is missed due to his Int bonus to AC, he is seeing that line of attack and the opportunity, and where and how he can move his body and weapon to avoid or intercept the attack.