I asked Plarium Game Support and received the following comprehensive answer:

To get 1 Soul Shard, you need to kill a certain number of units of the corresponding tier. Below, you can find the number of troops you need to kill to obtain 1 Soul Shard:

Тier 1: 1000
Тier 2: 500
Тier 3: 250
Тier 4: 142.9
Тier 5: 83.3
Тier 6: 55.5
Тier 7: 33.3
Tier 8: 12.5

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Good hunting😎