Are you trying to log in your Pi via SSH as ‘root’ or as user ‘pi’? Generally you shouldn’t have to set a root passwd (like Shoothere above said: use ‘sudo’), but if you did it shouldn’t generally be a problem. But how that is w/ Retropie and the Debian distribution on which it is based might be changed recently (I wouln’t know why, but hey).
Anyway, I would try to log in w/ the following command: ssh firstname.lastname@example.org.XXX
where 192.168.0.XXX is the IP address of your Pi on your (local area) network (see your router for said IP address). Could you copy/paste the error message of the command above?