You dont, you take the desktop version and use fraps for example.
but you didn’t say libgdx specifically… meaning you could just be using the android sdk.
I personally, would set up a good camera with a tripod, lights out - the way serious game reviewers record nintendo ds games for example
other than that maybe with a really strong tablet and some android recording software on there
EDIT: I just remember there are many desktop programs which take the video output of the phone and transmit it to the desktop via usb
because the remote apps work like this
you could record it that way, if its fast enough