Nothing in the game is missable, but I recommend starting working on treasure chests from the very beginning.
Castle Exnine (27 Treasures)
Note: This dungeon doesn't have a map, so I'll just put screenshots of the treasures and a brief description.
Ordeal 1 - Entrance of the dungeon, go forward from there, easy to spot.
Ordeal 1 - It's in the big pipeline, take the northeast path at the crossroad.
Ordeal 1 - Just before proceeding to the next screen, left side.
Ordeal 2 - After the section where you have to go up between two pipes, you'll spot this chest up there, take the small pipe at the north to get it.
Ordeal 2 - Hard to miss, it will be in your way to the third ordeal
Ordeal 3 - At the very start of this area, take the path up before descending.
Ordeal 3 - Just after descending from the last treasure, you'll find another pipeline, this chest is at the right dead end.
Ordeal 3 - A few steps ahead you'll see another chest at the distance, just continue going north to get it (the non visible part of the wall is climbable).
Ordeal 3 - When you get to this area, don't climb the "cube" just yet, instead, go to the right side to find another chest.
Ordeal 4 - From the save point, go all the way up, you'll fight a miniboss here. Once defeated, go north, you'll notice a hidden climbable wall with a chest in there.
Ordeal 4 - Now return to where the purple crystal is and go all the way to your left. (avoid the crystal, it's a shortcut to the entrance) You'll find a treasure in one of the pipes.
Ordeal 4 - Keep going until you find another big pipe, easy one.
Ordeal 5 - Another easy to spot, you'll see it from the entrance.
Note: There will be another teleporting crystal here, take it if you need and get Mirages that can get to 125 ice resistance and 11 weight. You'll need them in the next ordeal to get some chests.
Ordeal 7 - On your way to the top, after defeating the miniboss.
Ordeal 7 - When you get to the crossroad where you have to choose between going up and taking the pipe on the left side, go for the pipe.
Ordeal 8 - From the entrance, go all the way up
Ordeal 8 - Then go right at the second pipe.
Ordeal 8 - Now, you'll find another crossroad, with a cube to your left and a pipe to your north. Go north first to find 2 treasures.
Ordeal 8 - Now make your way back to the crossroad and climb the cube this time.
Ordeal 8 - Go all the way up from the last treasure, crossing the pipe to find another one.
Ordeal 8 - Take a few steps back, before crossing the pipe and go left.
Ordeal 8 - From here climb all the way down using the cubes, there will be a miniboss and a chest next to it.
Ordeal 8 - Make your way back to the previous chest and take the left pipe to find another one.
Ordeal 8 - Ok, it's time for some puzzling. Go all the way left from the last treasure to find a switch puzzle, complete it (125 ice resistance, 11 weight). Once done go a few steps back and climb down all the way to find another 3 treasures and the last ones of this dungeon.
You'll unlock this achievement after completing the following events:
Reached an ending.