How do I Manage Depth in a 2D Grid?

Like Pokemon or Zelda, it's 2D but when you're "below" something in the grid, you're in front of it, but when you're "above" it, you're behind it.

It seems impractical to create 20+ layers just for this. How would I make it so the above effect happens?

It's called Z-ordering, Z-sorting etc. use search with this and you will find few solutions.