In a thorough and complete manner; covering all relevant details and aspects.
From comprehensive (from comprehend + suffix -sive 'tending to') plus the adverb suffix -ly. This formation became standard in English by the 17th century.
Comprehensively is the adverb favorite of scientists and academics—when you present something comprehensively, you're claiming you've covered everything worth covering, which is a bold promise!
Complete word intelligence in one call. Free tier — 50 lookups/day.