How do I complete the Festival of the Lost 2019 secret Triumph?

Solution 1:

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.