Nothing in the game is missable, but I recommend starting working on treasure chests from the very beginning.
Nether Nebula (9 Treasures)
North from Gate.
Cavern 2 - On your way to the top, cannot be missed since it's required to continue.
Cavern 2 - At the end of the upper road, before you jump down.
Cavern 2 - After you've jumped down, by the left from the last treasure.
Cavern 3 - After the second switch puzzle, there's 2 treasure chests here.
Note: Earth Hammer is found in one of the chests here, required to complete "Best Helm in the Realm" sidequest.
Note: Skip the next part of the guide for now.
Smash ability required. Flutter ability required. I recommend coming back to this later, as you need to evolve a level 10 Copper Gnome into a Mythril Giant to unlock the required skill "Smash". and Flutter ability is a few chapters ahead in the game
Note: Copper Gnome can be caught in this area "Nether Nebula"
Secret Cavern - From Cavern 4 entrance, head to your right, you'll see a Stone which requires the "Smash ability", break it then use "Flutty ability" to get to the other side and reach the Secret Cavern entrance.
Secret Cavern - You'll find 3 chests in here, It's pretty lineal so just follow the road to find the first of them.
Secret Cavern - Not so far from the last location, you'll see a pair of chests at the bottom, just follow the map to reach there
Tip: I recommend capturing a Bablizz because you'll need his Chill ability very soon.