The primary way to collect shards is by using your Creatures to Reap. This action sacrifices their ability to fight for the turn but grants you 1 shard. Another common method is playing cards that provide shards, usually found in Action cards.

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Patch Notes v1.1.12
Dawnshard v1.1.12 brings major updates: migration to Thirdweb, a brand-new combat log, improved card graphics, redesigned menus, deck UI upgrades, and quest rewards UI.