Database

[{videos:[{"url":"","converted":true,/**...*/"resolutions":[{"file_url":"old_url.com/path1","details":{}},{"file_url":"old_url2.com/path1","details":{}},{"file_url":"old_url.com/path2","details":{}}/**{video_2},*{video_N}*/]}]}]

Query

db.collection.update({"videos.resolutions.file_url":{$regex:"old_url.com"/** oldUrl*/},"videos.converted":true},[{$set:{videos:{$map:{input:"$videos",as:"video",in:{$mergeObjects:["$$video",{resolutions:{$map:{input:"$$video.resolutions",as:"resolution",in:{$cond:{if:{$regexMatch:{input:"$$resolution.file_url",regex:"old_url.com"/** oldUrl*/}},then:{$mergeObjects:["$$resolution",{file_url:{$replaceAll:{input:"$$resolution.file_url",find:"old_url.com",/** oldUrl*/replacement:"new_url.com"/** newUrl*/}}}]},else:"$$resolution"}}}}}]}}}}}])

Result