Just completed one of these 'Assassinate the General' missions.
A couple of observations that may be helpful.
First - my style of play is that I like to protect my ship - damage is bad for business! (I respect other people's sty of play...

)
That being so, I like to play these tough characters by strafing runs, inflicting some damage with beam weapons, then retreating to allow my shields to regenerate.
So, I was rather miffed to get General <insert Russian name here> down to about 30% only to see him jump out.
I tracked him and killed him in another system, then was further miffed to find I didn't get a 'mission complete' - you HAVE to kill him in the specified system.
Then I saw someone in this thread post a warning that you should turn off 'Report Crimes against me' , otherwise the Cops jump in and might take the kill.
The penny dropped! - next time I turned OFF 'Report Crimes against me' before the battle.
I adopted my strafing tactics and the General NEVER JUMPED; I was able to whittle him to death
I think it may have been the cops jumping in that was scaring him off....?
Can't confirm this though, only an observation
Comments, anyone.....?
JJ