What were Hitler's and Mussolini's radical attitudes?
There is a bit of vagueness present in this question. In my mind, one of the most radical attitudes that both leaders presented was the open undermining of a liberally democratic or parliamentary style of government. There was little in way of attempting to work within the liberally democratic framework in both nations and in Europe, in general. The assertion of a "political superman" was radical in its open and brazen nature and Hitler and Mussolini were more than happy to make the case that they embodied this idea. The not so covert manner in which they advocated the dissolution of existing political orders in favor of structures that asserted their own visions was quite radical.
Another radical idea Hitler had was the genetic engineering of a new Aryan race of white supremacy, and the physical destruction of another. He set up camps for Aryan pureblood SS members to breed (The "Lebensborn Program")and encouraged them to have children out of wedlock, so that he could eventually produce a master race, even as he was murdering millions of "undesirables" in his concentration camps.
Mussolini's radical ideas included totalitarianism, where the government controlled every aspect of the economy, society, media and the state. While this was his radical ideal, he never really achieved it, at least to the degree they had in the Soviet Union.
This seems like a bit of a vague question...
I guess what was radical about both of them is that they were committed fascists. Fascism is a political idea that says that the whole country and society should be like one body. That means a couple of things.
First, it means that all the people should be the same. They should be the same politically and ethnically. That way they can all have the same goals and desires.
Second, it means that at the head of the body should be one leader with complete power, like how the brain commands the body.
That was pretty radical because there were not really any other fascist countries at the time.