There seems to be no way to export open tabs or bookmarks besides Opera Sync.
Even using Opera Sync the open tabs can not be handled user friendly and the Desktop-Opera cannot export tabs and bookmarks nicely (e.g. bookmarks.html standard)
I had this issue when I wanted to factory-reset my phone. I had ~ 65 open tabs which I did not want to be lost and I did not find a way to export those open tabs, even using Opera sync an a Desktop Opera Instance which I installed for that very reason.