For solar or arc lost sectors, use Eriana's Vow to defeat barrier champs and to drop any of the elemental shields. Equip your solar or stasis subclass (no matter the mission) - then use your dusk field or solar grenades to stun the overload champs. If there's a solar burn, I prefer the solar subclass because your super is also more useful to resist hordes or kill the boss. For void lost sectors, use the Black Talon void sword. It is effective both as a sword and to cast void bolts to kill the boss.