Is this a Caravelle unit?
You'll most likely have to lift the toilet off from its unifit flange and then tighten the bolts properly. You can only tighten the bolts so much by hand by reaching around from behind...that's if you have decent access from the side...which you don't. Atleast you won't have to mess with a new wax ring to re-set the toilet. It's too bad they didn't use fancy bolts like Toto uses on their skirted toilets that actually tighten from the top since there is no access.