Unstoppable Slasher does not have a counter on it.
Steps
Activate Blasting Station by tapping it and sacrificing Unstoppable Slasher.
When Unstoppable Slasher dies, its second ability triggers, returning it from your graveyard to the battlefield with zero stun counters due to Solemnity.
When Unstoppable Slasher enters the battlefield, Blasting Station triggers, untapping Blasting Station.
Resolve the Blasting Station ability from step 1, dealing 1 damage to any target.