the x-ray attenuation µ goes down with the atomic number Z going down;
in case of the photo-electric part of the attenuation by µ ~ Z3 *).
So, from your knowledge,
a) please select some candidates with high yield strength, which might fit your mechanical needs and after that
b) choose the one with the lowest atomic number from them.
To my opinion, Al (Z=13) and Ti (Z = 22) are such candidates.
But you may share your applicalion in more detail. A material with very low atomic number is for example CFRP (carbon fiber reinforced plastic); it has both
a) excellent mechanical properties and b) excellent x-ray transmission properties.
CFRP is often used in patient tables for x-ray examinations (e.g. CT).
With respect to 'compression' you may also think about boron-carbide etc. as x-ray window...