You keep pushing until it finally collapses (it is dirt, not rock).
In Mordred's underground laboratory, the wall to the left is just dirt and can be pushed down.
walk through
No mines. But there is an underground chamber in Arturus. And the volcano passages are underground. (see related questions)
You do not get or use a bucket on Astro Knights Island.
In the underground laboratory of Mordred, the wall to the left is not rock, just dirt. Push hard against it and it will collapse. (see related question)
There is no treasure chest on Astro Knights Island.
In Mordred's underground laboratory, the left wall is made of dirt and can be pushed through (with a little effort).
you push through
In Mordred's underground lab, the wall is just dirt. Keep pushing and it will collapse. This is the back way to the dungeon.
There are no bird eggs in astro knights island.
You don't. Once you have gotten the cheese, and pulled the wall switch, that is all you can do there. You will have to enter the dungeon from Mordred's underground lab, through the tunnel he dug to escape. (see the related question)
its on the island