This is how you do it. Have the Last word in your inventory along with your favorite crucible weapon. Use the auto or pulse rifle and charge your super. Wait until you can collect heavy ammo. Once you have heavy and a super charged. Equip the last word. Go on a killing spree with heavy and your super. Once you used up everything. Switch out the last word to your other weapon. Multi kills help you go up faster. You don't need kills with the last word. Just have it equipped when killing. Shotgun, melee, super, whatever. +1% for every kill -2% for each death you get. When I was completing the quest, it seemed that multi kills stack. So 3 kills may grant you 5%. But I am speculating on this. If you suck at hand cannons, this is my best advice. Don't kill up, the chaperone is a sweet shotgun. I torment guardians in the crucible with it. Get it quick, bungie is giving it a slight nerf in the December update. It's always in my inventory for crucible. Good at PVE, PVP is what it's made for.