History of Binary Stars

Binary Stars is awarded for completing the Exotic mission "Starcrossed" (30 points per the in-game data). Starcrossed is a Season of the Wish mission set in the Black Garden.

How to complete

1. When it launched, you unlocked it by finishing Week 4 of the seasonal quest "Wishing All The Best" and the preceding "Apophasis" mission, then speaking with Crow at the H.E.L.M.. Later it joined the weekly Exotic mission rotator (a source says this needs the Lightfall expansion and lists a 1955 power level for Normal and Legend), so it is now played from the rotator. The two sources differ on power recommendations (1810/1830 at launch), likely due to power-cap changes.
2. Collect the blue (Sire's Obligation) and red (Dam's Gift) light pools, each lasting 45 seconds; together they give Crowned by Dragons.
3. Work through the platforming, destroy the Obdurate Phalanxes in the correct symbol order, kill three Gatekeeper Wyverns, clear the jumping puzzle, and beat the boss Akardon, Pitiless Mind.

Rewards

Completing the mission rewards the Wish-Keeper exotic bow (first clear grants the Deepsight version). Related triumphs: Constellational Alignment (solo), Ahamkaraborn (Legend), Supernova Sprint (under 20 minutes). Which seal Binary Stars belongs to is unconfirmed. A search snippet quoted 5 points; the in-game data here says 30, so check in-game.