I wouldn't say that Elizabeth exactly hated the beach. She certainly liked it better than Campbell did at the same age. He wouldn't even sit on a chair on the blanket without screaming.
Elizabeth was just fine as long as her little feet didn't touch the sand. She was quite content stand at the very edge of the blanket and dig in the sand, always making sure that her toes never crossed the line. It actually made it quite easy to keep an eye on her - I always knew right where she was.
We eventually convinced her to sit on my lap at the very edge of the water and let the little waves lap over her legs, and she ended up loving it. Elizabeth would happily kick and splash in the water, but if her feet actually touched the sand, she'd scream - just like in the picture below.