Information about The Shells is mentioned in Sam's Journal.

If you haven't unlocked the journal yet you can unlock it by repeatedly clicking on Sam, the vector fish, located in The Depths until Sam gives it to you.

Hover over the spoiler below to reveal the relevant page in Sam's Journal.

Hint:
The hint for shell 1 was recently changed, if you had trouble before check it again, it's much more direct now.

Location:
The first shell can be found in the "settings & about" menu
Hint:
The second shell refers to a boss in the fight menu.
You can fight bosses by pressing the "Fight Boss" button.
There are different bosses for each area.

Location:
Shell 2 is obtained by fighting the Boss in the first area multiple times. It's a Catfish
Hint:
Check the only menu that has something to do with depth.

Location:
Shell 3 is located in the "Depths" menu, It should be in a corner slightly off-screen
Hint:
It's where you think it is, You might just not have a high enough level yet.

Location:
Shell 4 is located on the forge in the workshop, you need to be level 40 to unlock it.
Hint:
Sell a lot of buddha fish to the market.

Location:
It will show up as a purchasable item in the market at market level 25.