To open a secret chest, hold down --<~>
from the overhead view.

From here, you get a chest you must enter a code for.

Each chapter has a different code, here they are:

1. 6478
2. 9216
3. 7702
4. 2132
5. 5052
6. 0680
7. 0194
8. 4743
9. 9995