The reason it doesn’t say “skull damage” is because it is targeting a troop other than the one it is damaging.
I like the trait over Bullseye honestly. Consider the opponent’s troops each have 60 combined life/armor and your hero has 25 attack. With bullseye your first skull match has a chance to do an extra 35 damage. Your second match has a chance to do an extra 10. And if it triggers on 3rd match you gain nothing. But assassinate would add 60 damage regardless as the last enemy isn’t weakened.
Hero, Assassin, Mang (15 Brown/Red, remove target’s armor, gain attack equal to armor removed, do Magic + 1 damage)
Trigger Mang asap to get a big boost to attack, cycle with the others letting skull’s line up melting opponents, occasional Assassinate to clear from the back. I’ve used this with Archer class (losing the +5 magic b/c off color, but gaining Fast and 15% kill). Only problem is it dies to freeze.