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 :
You will see, This year I will graduate.
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.