As far as I can tell from the components, it means to show yourself hiding which makes no sense. Context is the sentence XはYに顔を覆ってみせる
顔を覆って == cover one's face (with both hands)
-みせる == that it was done largely to show other person(s)
X did it to show Y -- Sometimes it's fake (pretending to be sad, shocked, etc.). Other times, the "pretending" sense is weak or almost non-existent.
てみせる has other uses :
http://www.jgram.org/pages/viewOne.php?tagE=miseru
今年こそは修士論文を書き上げてみせる。今年、僕は大学を卒業してみせる。
You will see, This year I will graduate.
㋑強い決意を表す。「絶対に勝って―・せる」
So a better translation may be:
- This year I will graduate college, for sure.
- This year I will graduate from college, and that's a promise.
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The ~てみせる in the OP's sentence 覆ってみせる is definition #10-㋐「実際にその行為をして、人に示す」in デジタル大辞泉, while the ~てみせる in your examples 書き上げてみせる/卒業してみせる is definition #10-㋑「強い決意を表す。」. – Chocolate♦ Sep 28 '16 at 1:48