Your first choices should be "frightened of __" (general fear) or "frightened by __" (fear caused at that moment). I agree that "frightened with" is very difficult to use, because "with" usually suggests a person. The sentence would simply sound very awkward and unnatural.

with Difficult to think of a way to use that one.

I can think of ways to use the first three, but I'm not sure about the last one... 1. I'm frightened about failing school (i.e, I'm worried and scared that I won't be able to get a good job if I don't finish school with good grades). 2. I'm frightened that there may be a monster under my bed (i.e, frightened about the possibility of something) 3. I'm frightened to go out at night by myself (i.e, frightened to do something) and then there's number 4, for which I simply cannot think of a way to make sound natural!

You can say: She's frightened about getting pregnant. She's frightened that he could fall. She's frightened of sleeping alone. But you "frightened with" is not common You can also say "frightened for" I'm frightened For example: She's frightened for her children.