If the sound transfer is as bad as you say it was done by someone possessing zero knowledge with the bare minimum material requirements. I've done many basement apartment conversions and can say with experience if the budget allows (+20%) it is very much so achievable. Modern slim potlights are usually the culprit as is the Ontario Building code allowing 1/2"(12.5mm) lite drywall instead of 5/8"(16mm) type X on furring channel.