Stasis supers aren't the greatest for final blows. If you read the quest carefully you should notice that it does NOT require the super kills to be done with a stasis super. So any super should progress it. Only the one of the three parts requires a stasis subclass which is the stasis melee kills. The Shatter damage final blows can be done using stasis weapons such as the new exotic trace rifle. I would suggest equipping Monte Carlo and knock out your stasis melee kills. Then switch to whatever subclass you find you get the most kills with and equip one of the exotic weapons that freeze combatants. Use the weapon for shatter damage final blows and your super naturally for the super kills.