Heart of the City

Emblem was included with the Destiny 2 Armory Series 1 blind pin bags.

After the Nightfall

This emblem unlocks after you beat the Time Trial times of each Nightfall Strike; these times need to be obtained after Forsaken's release. The site destiny.report has a great tool to track your Nightfall times, I've included the link below. Thanks to the "DestinyTheGame" subreddit for figuring out the times for each hidden Time Trial. Likely no longer obtainable after the release of Beyond Light and the DCV.

Sonic Simulation

Purchase the Bungie Exclusive Gold Osiris Funko POP!

Aurelian Prize

Purchase an Armory Series 5 Pinnacle Weapon Collectible Pin from the Bungie Store.

Heretic

Any item purchased from the Bungie Store between 2017-12-05 and 2018-01-31 awarded this emblem.

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.

Time Dilation

Purchase any qualifying item on the Bungie Store during the Destiny 7th Anniversary (2021-09-09 and 2021-09-10 before reset).

Spectral Sea

In 2023: Donate $20 to the GCX Charity Marathon. Emblem code will be delivered after the event.In 2022: Donate $20 during the GCX 2022 streaming marathon, taking place from June 3rd to June 10th, 2022. An $80 donation option is available if you'd like to get both emblems. In 2021: Donate exactly $50 during the GCX 2021 charity marathon.

Empowered Voices

Purchase the International Women's Day Collectible Pin from the Bungie Store. The name of this emblem was changed from "Hebdomad's Crest" in v3.1.1.1.

Meridian of Destiny

Purchase the Destiny 2 Tricorn Collectible Pin; the emblem comes with the pin.

Circadian Guard

In 2022: Donate at least $10 during the 2022 Bungie Day Giving Festival.In 2021: Donate at least $25 to the Bungie Foundation during Bungie Day 2021.

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.

Gravitational Allure

Awarded for signing up for the Nordic website GameReactor.no

Long Slow Whisper

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

Bibliomancy

Purchase the Destiny Grimoire Anthology IV: The Royal Will. The emblem code should come on a card inside the book.

Brightwing

This emblem is given out by Destiny influencers during late 2021. Also awarded from the streaming site bilibili in late 2021 for watching Destiny 2 streams.

The Cleaver

Complete the Vow of the Disciple raid in the first 48 hours. The window of availability was extended due to raid connection issues.

Shattered Harmony

Purchase the Destiny 2: Beyond Light Original Soundtrack from the Bungie Store.

Apeirohedron

Purchase something from the Bungie Store during Season 13. This emblem is missing some info in the API, which is why it looks a little odd here.

Confluence of Light

Codes for this emblem were given out by Bungie at various conventions in 2017 as part of promotional appearances for Destiny 2's launch.