Did you get the mirror?
In order to obtain the mirror I have to have the shield to conquer the dragon. The shield is only available if I ride the condor.
I understand your confusion, but the shield is not
used to conquer the dragon. In very old versions of King's Quest, you could use the shield to bypass the ogre, but never the dragon - the shield melts under the dragon's fiery breath!
From Great Hierophant's own King's Quest I Version FAQ, posted on GameFAQs
The SCI version requires you to obtain the Magic Mirror and the Magic Chest before you can obtain the Magic Shield. Spoiler
The ogre guards the chest.
The dragon guards the mirror.
The leprechauns guard the shield, and you must ride the condor to reach their island.
You should collect the items in that order.