I did it weeks back and it took me forever. Rift was definitely the easiest because it had choke points. If you haven't don't it yet, though, I would HIGHLY recommend waiting till the next iron banner.
Yeah I know that's surprising but here me out.
I'm normal PvP there was times that I would put literally an entire clip into someone, every bullet registering, and they wouldn't die. It frustrated me to no end, more so than the black spindle mission the first time it came around (yeah I beat that the first night it was available). I still completed the challenge after a couple controller throws and have had the chaperone since that second week.
However, when I took my year two, 310 last word into iron banner, it was like night and day. I averaged over 20 kills a match, most of which were from the last word. It would down people an average of 3-4 shots. It honestly reminded me of how the last word was when I got it the first time in destiny back in September 2014 (back then few other people had it and the only people i would lose a 1 on 1 duel with were the few that had the original, pre-nerf mythoclast... That thing melted me).
So in closing, I would say just wait till the next IB. I know everyone wants the chaperone really bad... But to be honest, there are a lot of better legendary shot guns out there. The reload animation is fun to show off/use, but i really only use the gun when I'm not seriously playing and just want to have fun. Have patience and wait... Put your time into infusing a last word, and wait till the level advantages are back. You won't regret it.
Sorry for the length lol
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Very good advice right here as well :)
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Why thank you :)