While travelling with Rand, Asmo showed fear of two beings; Semirhage and the DO. (He wasn't even in awe of Lanfear, whom we know to be among the most powerful of the Forsaken.) What Asmo was really afraid of was pain:

"Another little present for you, Lews Therin. That shield will allow a trickle through, enough for him to teach. It will dissipate with time, but he'll not be able to challenge you for months, and by that time he will have no choice but to remain with you. He was never very good at breaking through a shield; you must be willing to accept pain, and he never could." TSR, chapter 58

Since we know that Semirhage eliminates herself from being the killer, and as far as we know, the DO doesn't have a physical form, we have to assume that someone else scared the be-jesus out of him.