Have you accepted your season pass rewards yet? As you level up, If you inspect your season pass you can click the point your on to claim the prize at each level. I think this progresses your triumph.
Basically each of this triumphs has 3 stages or tiers of progress you need to hit. For the artifact one, it’s asking you to get +5, +20, then +50 light.
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I think it's all becoming clear now. After I accepted all possible rewards on all three characters I was able to progress a triumph two, three, even four times. I had no clue the two were intertwined and dependant on one another. One question though if I may, the triumphs I cashed in prior to having the knowledge you provided me, in other words the triumphs that are grayed out but only show a partial score, will the rest of those points become available once I hit the next milestone it's asking for or am I locked out permanently because I didn't wait until all were met? Thank you for your counsel :-)
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On a side note, it would be very handy and helpful if someone privy to the different steps/milestones of each tiered triumph dictated them here or elsewhere on the web (even YouTube). If I'm on step 3 or 4 of one it'd be nice to know what I'm after versus blindly chasing unicorns and dragons. Especially with only 16 days left to complete the seasonal ones.
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I'm going to try that right now (Claiming all of the Season Pass rewards). I left a lot of the "Substitutional" armor and exotic engrams alone temporarily but the season ends in 16 days anyway so now's a better time than any other That may very well be the root of the problem, I'll keep you posted.