In a vigorous, forceful, or active manner; with considerable energy and determination.
From 'energetical' (or 'energetic') plus '-ly' (adverb-forming suffix). It's the standard adverbial form meaning 'in an energetic way.'
The fact that we can modify 'energetically' with even more adverbs ('very energetically,' 'quite energetically') shows English's flexibility—we can stack intensity upon intensity.
Complete word intelligence in one call. Free tier — 50 lookups/day.