You need to complete:
I recommend this order, since you need to finish some things first before unlocking others.
For example you need all the correspondences to get special items to then get all items.
Main story and fragment
all letter correspondences (start this as early as possible, it will always take some time for mail to arrive so start this right after the main story and then do other things in the meanwhile)
Complete all requests
Aquire all 48 ninja tools
10 Grandpa Gen trials
all friendship events (soon as you have full hearts for every friend and cleared everything else there is to do, just run around between the loading zones and the people should wait in front of the places. you really NEED to do everything else first, since some people may be occupied waiting at other places for you to finish request and therefore not be able to do the friendship events)