@080844
Your issue is definitely not the same as @Bubaliciouz issue. He did it with other players, which implies not Instant Action or Arcade, as none of these actually make you unlock the skin, although the steps are reproducible.
I don't know in Galactic Assault, but I tried in HvV and indeed it doesn't work. We shot at the portrait and nothing dropped, so the steps can't be reproduced in HvV.
However he got the message, and he can see the milestone completed in his Career Menu, so he definitely completed it. After that the last thing he needs to do is go to his Crates Menu and check for the Crate that has the reward.
As for you @080844 , just go to Co-Op and try again. EA Game Changer Elliot from the Battlefront Updates channel has reported he first did the steps in Single Player, which didn't give him the skin, but then when going to Co-Op he did it again and unlocked the skin. I did it in Co-Op as well.
So try Co-Op and then let us know if it unlocks the skin for you.