Mist Dragon's regular physical attack deals around 20 - 25 points of damage. It can dissolve into mist, nullifying all attacks against it. If attacked in the mist form it will use Cold Mist, which deals just enough damage to either kill both Cecil and Kain, or reduce them to low enough HP to finish them off.
The Mist Dragon is an easy boss. Cecil should use normal attacks, or Darkness, and Kain should use Jump. The dragon will use mostly physical attacks, and after losing some HP, it will dissolve into a cloud of mist. At this point the party should use Defend or just wait. When the dragon reforms, the party should continue the battle plan until the dragon vanishes into the ground.