Exotemporal

Complete the Vault of Glass "Tempo's Edge" Triumph, which requires you to complete Vault of Glass and all of the encounter challenges within the first 24 hours.

Long Slow Whisper

Complete the Deep Stone Crypt within the first 24 hours of its release.

Sign of Celebration

In 2024: Donate $7 and choose this emblem from the emblem vault during the 2024 Bungie Day period (2024-07-09 to 2024-07-29). In 2023: Donate at least $100 during the Bungie Day Giving Festival 2023.In 2022: Raise (not donate) at least $777 during the 2022 Bungie Day Giving Festival.Previously: Purchase anything on the Bungie Store between Bungie Day 2019 (2019-07-07) and 2019-07-13.

True Colors

Purchase the Bungie's Pride Collectible Pin from the Bungie Store. The API update for Shadowkeep (2019-10-01) changed this emblem's name from "On Our Shoulders" to "True Colors." This pin was retired when the Pride 2.0 pin was released.

Anomalous Signal

Purchase anything on the Bungie Store during Season of the Undying.

Disdain for Gold

Complete the Triumph "Season 7: Nightfall." This requires 25 Nightfall completions during Season 07

Stream of Light

Gift two subs to a Destiny 2 Twitch streamer who has the Destiny Twitch Extension enabled. Make sure you link your Twitch account to your Bungie account first! Emblem (and shader) will be available for pickup from Amanda in the Tower.

Emblem of Synth

Purchase any item from the Bungie Store during the Season of Opulence.

Death to the Deathless

This emblem randomly dropped upon completion of this Nightfall. No longer obtainable since this strike has entered the DCV.

Third Mark of the Collector

Purchase anything from the Bungie Store during Season of Arrivals.

Piratical Ambitions

Complete the Grasp of Avarice Dungeon solo without dying and redeem the associated Triumph.

A Sibyl's Dreams

Complete all eight (8) Nightmare Hunt Time Trials on Master difficulty on The Moon. You can find the Time Trial Triumphs in the Triumphs menu under Journey -> Triumphs -> The Moon -> Nightmare Time Trials.

Damage, Incorporated

Reach Valor rank Legend in Season 04.

Timeless Vigil

This pursuit has three steps to it, with multiple objectives in each step. The first two steps will give you shaders while the third step awards this emblem.

Crimson Echoes

Complete the "Savior of the Deep" Triumph on Earth's Moon by completing the Pit of Heresy dungeon solo without dying.

Atop the Spire

Earned by completing the Spire of Stars raid lair on Prestige difficulty. No longer obtainable since Spire of Stars entered the DCV.

Moments of Triumph 2021

Obtain 15,000 Triumph Score and redeem the Moments of Triumph 2021 Triumph, "Triumph Master."

Feast of Worms

This emblem randomly dropped upon completion of this Nightfall. No longer obtainable since this strike has entered the DCV.

Better Failsafe Than Sorry

These emblem variants can drop once you reach a certain score threshold in a Nightfall. The drop rates are unknown, but if you are looking to get this variant, you'll want to go for a high score run (get the highest score possible) in the related Nightfall, then do speedruns of the Nightfall until the emblem variant you want drops. Note this is a variant of the emblem named after the Nightfall it drops from.

Meyrin's Vision

Source: Solve the French glyph puzzle.