In Opera, goto the URL opera://bookmarks while logged in to Opera Sync with bookmarks set to sync. Then, ctrl + a in "Bookmarks Bar" and press del. Repeat for "Other Bookmarks", and "Speed Dial" if you want. And, delete any other bookmark folders you don't want. Then, empty the bookmarks trash.
Then, goto https://www.sync.opera.com/ and make sure it says 0 bookmarks. If not, you might have to wipe out all your bookmarks in any other Operas you have logged into Opera Sync and set to sync bookmarks. If it's still not 0, you'll probably have to reset your passphrase to wipe out all of your Sync data.
Another way to do things:
Goto the URL opera://about, take note of the "profile" path, close Opera and delete the "Bookmarks" and "BookmarksExtras" files in the profile folder. Also delete the "Sync Data" folder.
Then, goto https://www.sync.opera.com/ and reset your passphrase to wipe out all your sync data (which will include bookmarks).