If you want a cheap flight from Dublin to Shanghai, you've got zero airlines to choose from.
Make sure you use the search options above to search for flights to other airports in Shanghai, not just Shanghai Pu Dong Airport. The more options you look at, the better your chance of finding a cheap deal.
During this peak season, accommodation prices often increase too, so it's best to book early. Or you could keep your fingers crossed and hold out for a last-minute deal.