How to report how a filter was designed (scientific papers) + how to calculate filter attenuation?
Five of those (low/high-pass, cutoff freq, and IIR/FIR, how the filter was designed, attenuation) can be easily described using words or numbers.  The others (phase response, transition bands) are often better described with a picture.

I would recommend describing those five "describable" characteristics and, if appropriate, put pictures of the phase and magnitude response along with the actual filter taps in an appendix or something.