I know the all-time record score is 149-0 (which was in a game in Madagascar where the losing team deliberately scored own goals in protest at refereeing decisions, so it doesn't count for these purposes!), then the next highest I think is all the way back in the 1800s between Arbroath and Bon Accord in the Scottish Cup, I genuinely wonder if they managed as many shots in as that!
From a very quick google search the most I can find is that Atalanta had 47 shots in a Serie A match in 2019 and scored a grand total of 0 goals. I'm sure it has been beaten in Sunday league or youth football or sometime before they counted shots though.
