The meaning of the idiom “to have a whale of a time” alludes to the largest mammals on earth and describes that you experience and enjoyed a “great” and “impressive” time. Whether the
origins of this idiom are not clear it describes for me very vividly the feelings and impressions I experienced when I went out to encounter these magnificent animals.
During these "eye-to-eye"-encounters the time really stands still for a while. You stop to breathe and forget to trigger the camera. This privilege is a "once in your
lifetime" experience.