It's tricky because the quest makes you want to play cautiously, but the TLW does not excel with that play style. TLW still melts guardians at close range, and I had trouble with this part of the quest until I started playing aggressively. You have to be smart about. Only get aggressive in 1v1 situations, don't rush 4 enemies (unless you plan on using your super) that won't work lol. But TLW still outguns almost everything in its optimal range, get in close, but stay just outside of shotgun range and you'll be golden. Regardless of how you finish it, I do wish you luck getting the quest done.