SEMI SPOILERS FOR REALZOnce you beat the final boss you unlock a new option in the phone menu where you can revisit any day of any week at any time. This is the way to get all hard/ultimate drops for all the monsters/bosses you fought before you unlocked that difficulty. Also you can choose which partner gets to fight with you at anytime.
Also unlocked (if you got some secret reports or something) is ANOTHER DAY, which has the hardest enemies in the game. Here you can challenge most of the characters to a game of "tin pin slammers" (marble slash was such a better name

) and get some REALLY good pins, like the best of the best. Vortex Slash

Anyway there are also 2 optional challenges in another day:
one, while looking for everyone to play the tin pin minigame with you, go down to near where the end of the game took place (sewers) use your mind reading badge (black skull) and you should see a door appear much like before. Enter it (no turning back unless you use the phone menu and redo another day) and you should see a certain familiar someone.
Talk to this person and you will enter a boss rush mode. It is damn near impossible so be very prepared... you fight like 9 bosses or something in a row. Bring a healing badge!
I think you get one of the best pins for beating it, and maybe some other stuff.
lastly, if you think you want an even harder challenge, go to PIG CITY (its to the very left of that soup shop area) and fight your way to the highest floor. On each floor you are limited to a certain brand of pins + the unbranded ones.
At the top floor is an optional boss who is supposedly the hardest in the game. He gives you a pin which evolves into the best pin after a while. I dunno I cant make it to the top
