Tableau can return a calculated field that concatenates the hierarchy field values for you (eg. if you hierarchy was country > state > city, it could return "USA, FL, Miami" in one field). However if you want to return three separate fields for each level in the hiearchy, then you'll need three calculated fields.
To describe what you're asking for, you could set up three calculated fields like this:
Field 1 (I assume this will always be shown so no logic needed here - you could even simply use your level 1 field)
if [Pick Columns] = 'Level 2' or if [Pick Columns] = 'Level 3' then [Level 2] end
if [Pick Columns] = 'Level 3' then [Level 3] end
You can then add each field to your rows or columns shelf.