In order to unlock Anarchy's Executioner, you have to defeat every boss with your Killer Weapon. It doesn't matter if you use a weak or strong attack, just so long as your holding the right trigger to activate your "Killer Weapon." You'll not you got it when you get an Overkill! +10000 bonus with your final hit.
The sequel to the award winning Hellblade: Senua’s Sacrifice, Senua returns in a brutal journey of survival through the myth and torment of Viking Iceland. Intent on saving those who have fallen victim to the horrors of tyranny, Senua faces a battle of overcoming the darkness within and without.