Atrociously means in an extremely bad way. You put it with a verb, or before an adjective: she sang atrociously; the room was atrociously hot. Like atrocious, everyday English uses it for quality — badly done, badly behaved in a messy way — more than for cruelty. It sounds strong and a bit theatrical. Very badly is the calmer cousin. Though actually, next to a verb like behave, it can still lean toward 'in a shocking way,' depending on the sentence. It does not go in front of a noun: atrocious weather, not atrociously weather.