Recurrent Resplendence

Purchase the Loot Crate Limited Edition Destiny 2 Crate (the first Crate, not the one that came with Matrix Jubilee).

K1 Revelation

Purchase the Destiny 2: Shadowkeep Collector's Edition. The emblem code will come on a card in the package.

Cryptologist

Solve the Cryptoglyph puzzle in the Destiny 2: Shadowkeep Collector's Edition.

Day of Seven

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.In 2018: Purchase any item on the Bungie Store on Bungie Week (between 2018-07-07 and 2018-07-14) and this emblem will be awarded.

First to the Wild

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

Little Light's Emblem

Purchase an eligible vinyl Ghost shell figure. The following vinyl Ghost shells are have the code included, as of so far: Moon of Saturn Shell and Sundance (Cayde-6's Ghost). As of early 2021, these don't appear to be readily available. If you purchase one second hand, please make sure it comes with an emblem code.

First to the Forge

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

Hellspawn

Purchase one of the Spring 2018 McFarlane Toys line of Destiny 2 action figures. The Ikora Rey, Zavala, and Cayde-6 figures come with the codes. These can occasionally still be found out in the wild, but be careful of people that open the box for the code, then resell the figure by itself.

Anomalous Signal

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

Answered Call

Complete the Triumph "Super Celebratory" during The Revelry 2019. Once complete, redeem the reward from Bungie Rewards.

Peace of the City

Purchase a Destiny 2-branded can of Rockstar Energy and use the promotional code. The emblem code should be sent to you upon using your first promotional code.

Carrhae

Purchase the "Destiny Ghost Vinyl - Generalist Shell" and the emblem code will come in the box. As of early 2021, these Ghost Shells don't seem to be readily available. You may still be able to find them second hand, but please make sure any ones you buy come with the emblem code.

Emblem of Synth

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

Leviathan's Feast

You'll need to open a ton of "hidden chests" on Nessus; these are the chests littered around the planet. Unfortunately, no drop rates are available.

Dark Orbit

Finish the first quest for Festival of the Lost 2019, then redeem the offer in Bungie Rewards. Only available during Festival of the Lost 2019.

Infinite Possibilities

You'll need to open a ton of "hidden chests" on Mercury; these are the chests littered around the planet. No longer obtainable since Mercury entered the DCV.

Tactician

Complete the Vanguard quest "Honor Bound" during Season 09.

Savior of the Past

In the Corridors of Time, follow this pattern: Diamond, Clover, Snake, Plus, Hex, Hex, Plus, Hex, Diamond, Clover, Snake (Credit to /r/raidsecrets).

Timeline Warrior

Complete your first run of the Sundial on Legend difficulty.

Vex Convergence

You'll need to open a ton of "hidden chests" on Mercury; these are the chests littered around the planet. No longer obtainable since Mercury entered the DCV.