Go to Tools>Preference>Advanced>Browsing and uncheck tootips. Or if you want to keep some of the functionality of the tootips but just get rid of the hover link address do this:
I think the bit about changing all of the tooltips changed with the latest edition of Opera. I had to follow the path I outlined first to get to the tooltips box. The bolded stuff is what to do if you want to only get rid of the link addresses–>change the 1 that is probably there to a 0.