You have to get 10 A+ catches for any species to get a plaza ticket. After that, the only thing you get is in-game medals for various fishing spots. For instance, if you've caught all types of fish in a fishing spot, you'll get a bronze medal for that spot. If all the fish you've caught there are, I think, B grade or higher, you'll get a silver medal and if all fish caught there have an A+ rank, then you get a gold medal for that spot. Once you've beat the game and acquired the streetpass hat for beating all the islands, these medal requirements are added to the list of challenges for the game and will give you in-game rewards.
While part of me would like to beat the game fully like that and accomplish all challenges, I don't think it's going to happen so I might as well get my plaza tickets and get out. However, someone I've streetpassed looks like they may have done it because when going through the rankings by species, they seem to have an A+ for almost every fish. Seeing that made me wonder if I was missing something. I still need to finish catching everything because I'm missing some of the rare species which is another part of the game design I've come to dislike as well.