Had a look into this today, but reproducing your situation as closely as possible from the video (wearing the same 5 items and ring, prereqs met for Cement His Torment), I always successfully complete the achievement.
It's definitely not down to your equipment - you need to be wearing 5 or more black armour items (cosmetic overrides make no difference; it only checks your worn equipment) in order to attack the wraith.
And I saw from your video that the wraith dropped a black platelegs, which is after the achievement complete code, so it's not breaking early.
So from that evidence, the only condition that might be failing is the "findhero" check to get the player who did the most damage in focus, to complete your achievement.
I'd suggest ensuring you aren't in a group or friends chat with lootshare enabled, and don't have some external means of damaging the wraith, like a combat familiar. (Didn't see one in the video, so that's a long shot.)
If that doesn't help, please send a bug report if you haven't already, so we can get your RSN and repro by cloning your account. (I did my best to find it out from video - best I could tell it's Vant Dragon, but that wasn't a recognised displayname when I looked it up.)
Thanks for the video, by the way. That was a huge help in ruling out potential causes!