Unless you don't have access to any data from your previous OS install, I think the only chance is if you've used Opera with your sync account on any other computer. If so, you can check if either the "Bookmarks" file, or the "Bookmarks.bak" file contains the bookmarks you're missing. The folders are in:
Windows: C:\Users\ username
\AppData\Roaming\Opera Software\Opera Stable\ (If you've also logged in on a windows PC)
How you then restore them is a good question, but I guess you can just try to copy the "Bookmarks" file to every installation you have and try to make sync not delete the bookmarks.