Medieval technology might not allow for direct "arrow-proof-glass", but what about periscope helmet?
Since arrows travel in approximately straight lines and cannot follow curves and bends, a helmet with an indirect visor, using mirrors, could prove useful. This idea basically comes from existing inventions like periscope glasses, periscope rifles/cameras and trench periscopes.
Proper silvered-glass mirrors did not exist yet, but simple glass mirrors did exist.
Example of a WW1 trench periscope, imagine a tiny version of this mounted on a helmet. There will not be a direct line in which an arrow can hit a knight directly in the eye.
But there are some disadvantages:
- Worst case scenario the arrow hits in the "artificial" eyes and
destroys a mirror, to avoid immobility make the helmet so that the periscope part can be detached (this adds some flexibility).
- Obviously a knight watching through a periscope will have to deal with limited sight.
- Depending on the precision of the periscope and the mirrors inside the hand-eye coordination could prove to be slightly more difficult.
Side note: Bascinet helmets have incredible small eye-slits, I know they are not made from glass and are far from perfect when it comes to vision, but maybe worth checking out?