Hey Rafael, how are you? As far as I know, the idiom ''beyond a shadow of a doubt'' is correct and is commonly used in conversation by English speakers. This expression means the same as ''with confidence'' / ''without any doubt.''. So, regarding your example, you could just as well say ''I believe, without a doubt, that she is innocent'' or ''I undoubtedly believe that she is innocent'', and the meaning would still sound the same. Here are some other examples: ''This photo now proves, beyond a shadow of a doubt, that my client is innocent.'' ''I barely remember leaving the office last night, so I can't say beyond a shadow of a doubt that I set the alarm before I left.'' ''His guilt was established beyond a shadow of a doubt" Hope that helps!!!

Yes. It's clear, it's normal, it's correct, it's natural. It is slightly colorful, slightly formal, slightly elevated in tone. It expresses a strong opinion. "Is she innocent?" "Yes, she's innocent." "Is there any doubt about it?" "There's no doubt about it." "Really, no doubt at all? Not even the slightest bit of doubt?" "No, she's innocent beyond the shadow of a doubt." As a quick verification, I tried a Google News search on "shadow of a doubt" and, as I expected, got dozens of hits. The British environment secretary said ""It could translate into meat being in shorter supply and prices having to go up because the cost of production is going to have to go up, without a shadow of a doubt." A local newspaper in Wheeling, West Virginia, said this about a high school football player: "On easily the biggest stage of his career, Monroe Central’s Ryan LaFollette proved beyond a shadow of a doubt he has what it takes." _Newsweek_, in an article about Beyonce's best recordings, said there had been questions about her at the beginning of her career, "but the fifteen intervening years have proven Beyonce’s star power beyond a shadow of a doubt."

Yes, it's a very strong way of emphasizing your point and your example sounds completely natural.