Terns eat Krill
Krill uses extensive Chitin
Chitin Bio-Magnifies Radiation

Looking for radiation in the eggs is probably barking up the wrong tree.   Seeing if Terns are dying from radiation or starvation is the most likely 2 paths.

Scientific proof is here

http://nukeprofessional.blogspot.com/2016/07/is-fukushima-radiation-demise-of.html