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In-gamewise, there's no indicator of what the Secret Triumph is. There is a Secret Triumph, although both the objective and reward are hidden. However, using a tool like Braytech or Destiny Tracker shows what appears to be the actual triumph:

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Now according to this, the secret triumph requires me to see a spider in my sights. I don't believe this pertains to the NPC Spider of the Tangled Shore considering a few things -- one, your weapons are disabled when you are in line of sight of Spider, so you can't scope in on him or even aim your gun at him. I remember back in Destiny 1 where as an easter egg, aiming down sights had a chance for a spider silhouette to crawl across your screen momentarily. I've played around with scoping in for large amounts of time and have not seen anything.

In any case, how do I complete this secret triumph for the Festival of the Lost event of 2019?

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The activation window for the Secret Triumph was activated as of the Weekly Reset for 11/12/2019.

The only criteria to obtain the achievement is to just aim down your sights. When you do, there is a small chance for a spider to crawl across the screen, similar to Destiny 1's spider jumpscare. When that happens, the triumph is unlocked! Note that you can do this in any activity, like a Crucible or Gambit match, and even in Nightfall strikes.

For players looking for a more consistent way to proc the triumph, using one of Eva Levante's new consumables (boosts Strange Choco Coin gains in Haunted Forest) in the Haunted Forest itself, then aiming down sights for a while seems to do the trick as well.

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