I have completed forsaken 3 times, once on my hunter and twice on my warlock after i deleted him to see if that fixed it. I got destiny 2 when it was briefly free on battlenet and came back when it went free on steam, got addicted and brought forsaken and shadowkeep, when i killed the rifleman for the first time did not get any triumphs so when the tangled shore was the flashpoint did the adventure and killed him to get the triumph but did not get the lore triumph. I have the triumph for killed all of them as well.
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This happened to me when Forsaken first released over a year ago. I too had completed the campaign on all three characters, but that particular Triumph did not trigger. What ended up triggering it was re-running it as a Heroic Adventure when Tangled Shore was the Flashpoint location.