The only way to get the seasonal weapons is by owning the Deluxe Edition with seasons 12-15. This will allow you to obtain The Hawkmoon from season 12 and Dead Mans Tale from season 13. Other game prerequisites will apply like having Shadowkeep and unlocking the tangled shore.
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Is there not a single way to pick these seasons up individually? £60 is pretty obscene for a few guns.
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No, the only way is by the Deluxe Edition.