Through the Heart

Purchase something from the Bungie Store during Season 10, Season of the Worthy.

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.

Blood of Izanami

Complete the "Reunited Siblings" Triumph, which required you to kill 500 enemies with Izanagi's Burden at the Izanami Forge. No longer obtainable after this forge entered the DCV.

Blade of Bergusia

Obtained by completing the "Clean Up on Aisle Five" Triumph, which required you to kill 500 enemies with Threat Level in the Bergusia Forge. No longer obtainable after this forge entered the DCV.

Vengeance of Volundr

This Triumph required you to get 500 kills with Jötunn at the Volundr Forge. No longer obtainable since this forge entered the DCV.

Vex Destroyer

Obtained by equipping the full "Kairos Function" set on a Titan. No longer available as a result of Mercury entering the DCV.

Secrets of the Vex

Obtained by equipping the full "Kairos Function" set on a Hunter. No longer available as a result of Mercury entering the DCV.

Transcendent

This emblem will drop upon completion of the "Ascendant Paragon" Triumph, once you complete all six (6) Ascendant challenge time trials.

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.

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.

The Next Chapter

Complete the Season 13 Triumph "Tale Told," which requires you to complete the "Presage" mission on Master difficulty without dying. This emblem was retired at the end of Season 15.

Cartomancy

Complete the Season of the Witch (Season 22) Triumph "Arcane Knowledge," where you need to identify all of the Minor Arcana at the Lectern of Divination.

Meyrin's Vision

Source: Solve the French glyph puzzle.

Visio Spei

Obtained via the following universal code: 993-H3H-M6K

A Forest of Red

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

Obsidian Dreams

Complete "The Lost Souvenir" quest. This requires you to solve the "Lost Datapad" item. No longer obtainable after the forges entered the DCV.

Satou's Secret

Source: Solve the Japanese glyph puzzle.

Woodland Warband

Reach Iron Banner Rank 16 in the first reward track during Season of the Witch (Season 22).

Strike Operator

Complete the Vanguard seasonal quest "City Defender" during Season 10.

Rasmussen's Gift

Source: Solve the Norse glyph puzzle.