Her dad has quite unrealistic expectations if he expected his daughter to beat an NOL Colonel, who's probably got years of experience fighting people just as strong as her. Unless he subscribes to the Azrael school of thought in that physical strength's all I need, who needs training.
Which brings me to the next part, I don't know why, but I'm getting the feeling that the whole "was able to physically repel Azrael by just himself" was him being the last man alive of whatever squad he was in and Azrael either decided he had his fill or got bored/disappointed with who he was fighting and in the aftermath for propaganda purposes, the NOL elevated his reputation to 'Hero of Ikaruga' levels.