示す: 1. to (take out and) show; to demonstrate; to tell; to exemplify; to make apparent, 2. to point out (finger, clock hand, needle, etc.), 3. to indicate; to show; to represent; to signify; to display.
見せる/みせろ: 1. show, 2. display.
I can't find any references related to 示してみせろ, except in a song by a Japanese band Lustknot. "Decayed My Skin". One of the fans translate 示してみせろ as "show a sign", but it's not quite fit the sentence I found in light novel.
I'm confused with the 2 words with an almost similar meaning put together into a word. I have a feeling that it simply means "to show", but it's like an emphasize, and perhaps "to show (with enthusiasm feeling)".
Thank you for your kind guidance.