I agree with you on they should have an alternate method instead of forcing players into PvP for what seems a quest step not in line with the other requirements. However, since Momentum Control is returning to the PvP rotation, I believe you could use that to finish the 50 kills for the quest. Unlike other PvP game modes in the Crucible, Momentum Control only take one or two shots to down an enemy combatant. Shields are essentially irrelevant. I suggest you try that mode for progress. Stay with your team/use them as cover, hug walls and corners, use grenades to soften up targets or control a space before using the sidearm to take the shot. It may take quite a few games to finish, but I believe this mode will be easier for you to succeed in. I finished the Jade Rabbit and a few other catalysts in this mode. Whatever your decision, good luck out there!