To copy a hierarchy from Advanced Planning for Jira Cloud, the only mapping you need to configure is the Parent mapping
This will take care of all levels, from Initiatives and Epics to Sub-tasks.
To create a hierarchy in Advanced Planning, you also need to map a custom text field to Issue Type and populate this field with the desired issue types. That will let Ceptah Bridge to know which type of issue to create. If a task should have the default issue type, the field can be left blank.