So I'm currently at this quest with my main character, which is an air/water mage. Since one of the opponents is immune to physical damage while the other is immune to magic damage, does this mean I have no other option but going back to the Lady Vengeance and rebuild my champ as a hybrid character because the quest is impossible to do?

As a physical champ I could toss grenades or as a ranger, shoot elemental arrows to deal with the physical resistance opponent, but as a mage I seem to be royally screwed on this. Who thought this was good quest design and how drunk was the team when they implemented it into the game? So much for identifying with your game character when you are forced to rebuild it because of bad quest design...

As I mentioned in your other thread, I had no trouble with the fight playing my main as a support build. My deity ran over and stabbed the void creatures while my Incarnate handled the physically-resistant one. So take out the one that's vulnerable to magic and let your deity kill the other. You should be ok.