На духу (церк.) - на исповеди. Как на духу (·разг. ·устар.) - откровенно, чистосердечно.

the original meaning is similar to 'as if during confession (as in catholic or eastern orthodox church)', the meaning откровенно, чистосердечно (frankly, honestly) developed from the original one,

but this word is archaic, i wouldn't know it without consulting the dictionary, and I doubt many Russians would be able to say what it means without looking it up in the dictionary.