This question's far too broad, but I'll try my best. First, in the bottom floor of the dungeon (where you start), in the area with several npcs, you need to check a box on the right side to open a secret passage. Talk to the npc there and get the item on the treasure chest. You'll have to keep coming back to this area regularly as more treasure chests will spawn as you advance the game, and one of those has something you need to give to an NPC at the arena to gain treasure 9. This is missable because if you beat a certain arena boss without doing it, you won't be able to anymore.
Another missable is Treasure 14, located in one of the rooms in the arena, but will become inacessible after doing the very first arena fight, so just explore the place before fighting. There's also 37, which you won't get if you fight a certain series of bosses out of order. Just explore every area throughly and you shouldn't have a problem with it.
Then there's treasures 33 and 34. I believe 33 is in the sub-area you get to by stepping into a magic circle while having a black magic core and wearing the school uniform outfit, which you cannot return to after you complete the events there, so just be thorough in checking. While 34 is when you're exploring one of the sub-areas in the first floor (the east one), which is another place you can't return to, so same deal.
Technically Treasure 1 is also missable, but only if you completely ignore the pink-haired girl and don't talk to her after defeating her.