Don’t sweat the PvP stuff
There are 2 major steps involving PvP. First, to get kills and second, to get 25 Blood for Blood or Best Served Cold medals in the Crucible. For the first step, kills and assists add 2% to your total and dying sets you back by 1% each time.
The trick for this is to grab a well-rolled Bygones (or Go Figure, Blast Furnace, or Chattering Bone) and play the most cautious two games of your life. Stick with teammates, tag every opposing Guardian you see, do not venture off alone, and generally play to the pulse rifle range. There are a lot of hand cannons and scouts in the game right now, and some incredibly good Polaris Lance wielders, so as long as you play cautiously you’ll be fine. I’m absolute garbage at PvP and I got this done in two games by just being hyperaware and hypercautious.
(Don’t crouch in corners, though; the Last Word is an honourable man’s gun and that should not be how you get it.)
The second part was trickier – I think it took me three or four games to complete. You need 25 medals total and they come from either killing a Guardian who last killed a teammate, or killing the Guardian who last killed you. Of the two, Blood for Blood medals are much easier to get. Hang with teammates, let them take gunfire, and clean up as best as you can. (Not as honourable as I would have liked but, eh, you do what you gotta do.) You’ll get anywhere from five to ten medals per match so if you make it a point to group up and run around the map, this may take as little as two games.
Both are surprisingly easy to do – I think the Chaperon quest with the elemental kills took me longer – and the whole quest overall is about 3 to 4 hours of work depending on how well the PvP stuff goes and how frequently the Witches’ Ritual event spawns.
For the mission, play a subclass that can heal
The mission has the Attrition modifier switched on – you regen painfully slowly, but enemies can drop wells of Light when they die that heal you up quickly. It isn’t difficult, but it is a really annoying modifier, especially in a mission that has a decent serving of Knights and Wizards.
I played a bottom tree Striker Titan because who doesn’t want to regenerate with every punch, but top tree with Shoulder Charge and An Insurmountable Skullfort will work just as well. For other characters, I imagine Devour Warlocks will survive through anything, but I have no idea what Hunters should do.
This isn’t essential, mind you; you can just as easily play without the ability to heal and as long as you’re relatively cautious you’ll be just fine. But I like to play recklessly and the ability to heal on kills was very handy. For that same reason, Crimson will serve you very well here if you don’t want to run another exotic weapon.
And about that final boss …
Spoiler incoming for the boss mechanic of the mission that gives you the Last Word. Skip this entire section if you don’t want to be spoiled. Still here? Okay then.
You need to shoot the gun in the boss’ right hand. There are three phases total. You stand on a plate, the boss spawns, you’ll see a prompt that says ‘Ready’ and then another prompt to ‘Draw’. You’ll draw the Last Word and you need to shoot his gun – his whole right arm will glow when it’s time to take the shot, so you’ll know – and he’ll be visibly staggered if you’ve done it correctly.
This needs to be repeated a total of three times – first one of the boss will spawn, then two will spawn, and then three will spawn. You need to shoot each of them in the order that they spawn in. Failing to do so will kill you instantly and you’ll need to restart from the nearest checkpoint. There are also no checkpoints after each round, so if you fail on the third (for example) you need to repeat the previous two.
While this isn’t super painful, it does sometimes seem to bug out. I can’t tell if it’s lag and my network is the problem or if the fight is just a bit glitchy. But, essentially, sometimes you’ll get the shot off, the boss will stagger, and an instant later his shot will hit you and you’ll die. The only thing you can do is stick with it.
Also, don’t hipfire. I fell into that trap and either my second or my third shot would go wild as I gave in to brief panic. So although it may be tempting to hipfire the Last Word, ADSing makes landing those shots on his hand a heck of a lot easier. (I also imagine this isn’t a problem on PC when you have a mouse to aim with; I’m on console with twin thumbsticks, so ADSing was much safer.)
Spoiler ends here.
So, yeah, that’s really it
It’s a short quest and completing it will get you the Last Word. It is exactly how I remember it in Destiny 1. It’s not going to replace the Kindled Orchid or Midnight Coup in PvE, and it probably won’t replace the Ace of Spades or Luna’s Howl or Not Forgotten in PvP. But it is a damned good weapon, it is a heck of a lot of fun to use, and it’s surprisingly easy to get. So, really, unless you absolutely despise PvP, there really isn’t any reason not to go after it. And if you do, good luck.
P.S. Also read the lore that comes with the quest. It’s good stuff.