Complete the Exotic mission "The Whisper" on Legend difficulty.
Launch the mission from the "Into the Light" subscreen on your Director.
Complete the Exotic mission "The Whisper" in Pinnacle Ops with a performance grade of A or better, or complete the mission from the Legends subscreen on Expert difficulty.
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With the Blights dealt with, you need only complete your journey through the Taken anomaly to imbue your Whisper of the Worm with additional power.