Every way to collect hero shards: shop chests for emeralds and bottles, map milestones, the Altar and other rewards, plus a lookup for any hero.
Every shard hero has its own shards. Collect enough of one hero's shards and that hero unlocks; more shards raise its rank later. For example, Na'Ziba unlocks at 10 shards.
A shard pack is one random draw: it gives shards of one hero from that chest's list.
Every size costs 5 emeralds per pack, so bigger chests are no cheaper; they only appear as you climb the map.
Bottle chests cost 40 bottles per pack at the small sizes.
Each chest has a "likely", an "unlikely" and a "rare" hero list, plus a small chance of a whole hero. After floor 1500 the shards per draw go up, for example from 1 to 6 shards before 1500 to 10 to 15 after.