Blacksight is the Slow-mo ability that you will be able to use in certain chapters. The meter recharges by killing enemies.
The 5 headshots don't have to be in one Blacksight which makes it pretty easy to get by reloading a checkpoint.
Go to Chapter 3 / Scene: Roles reversed. In this firefight you can easily run up to the enemies, activate Blacksight (L1) and shoot 2 or 3 enemies. You can't specifically aim for the head but it will happen naturally after a few shots. Reload the checkpoint and repeat, the Blacksight meter will be filled up again.