I completed the first step of introduction to combat but this was not acknowledged by the NPC
Character name is Luke
Looking into the data, it has not recorded the kill that you need to make for him to complete the mission. (I am not doubting that you killed it, but it has not recorded it)
Can you try with this character to kill the required enemy again, and let me know if it fails again to record it.
While in combat, keep an eye on the npc mission, as it should show a green icon once the required enemy has been killed.
Luke just destroyed a Bruwar class scout but the mission log did not go green. There is still some debris in the asteroid field belonging to the scout.