Quartus will attack with magic, so using Deflect/Protect Magic is recommended.
All the Legiones share the same Special attack, they shoot a ball of lightning into the air and it will land on the ground in a 3x3 square area lasting for 3 seconds. If you stand in its area of effect you will take constant damage for around 2000.
Each of the Legiones have a special effect each 25% of their health they lose (75%, 50% and 25%) for Legio Quartus he will teleport you to a square right next to him. When he does this, simply run away again carry on with the fight.
The best way to beat quartus is to keep moving, once you have him targeted you can run around his room in a circle pressing your abilities. Try to avoid using combo abilities as they will prevent you from moving and you will be hit by one of the lightning balls and take a lot of damage.