Soul Shard

Material

A soul torn from a fallen boss and crystallized. Certain merchants trade for nothing else.

Lady "Shadow"
Mystery Vendor in the City of Tazan, City of Aldenreach and City of Veldak. Sells Mystery equipment for Soul Shards.

Boss encounters
Every cleared boss encounter gives 1 per full 10 levels of the boss (at least 1), x 1.5 on Nightmare and x 2 on Inferno, rounded down: 10 on Nightmare and 14 on Inferno, where bosses are level 70. Mini-boss stages give none.
Mythic Rift boss
7 + 0.5 per tier (up to tier 100), halves rounded up: 8 at tier 1, 32 at tier 50 and 57 from tier 100 per cleared boss encounter.
Lucky Wheel
24 per win, 6.69% chance per spin. A spin costs 10,000 gold.
Salvaging equipment
Always from Divine equipment. 10% chance from Common equipment. 20% chance from Uncommon equipment. 40% chance from Rare equipment. 70% chance from Legendary equipment.

Drop chances are the game's rules for offline characters; the game server decides the loot of online characters.