Longblaster Rifles are those used by the specialist class and are the sniper rifles of Star Wars.
To access the specialist class, choose Specialist when selecting your loadout when in a game as seen below. There are 4 Longblaster rifles in the class with one being unlocked by default.
The kills can be gotten in any game-type where you can access the Specialist class and are cumulative across all matches.
I would suggest playing Galactic Assault (20vs20) and posting up in a position overlooking the objective. I had a lot better luck getting the kills defending. IQA-11is the 4th sniper you can get in the specialist class and is capable of a 1 shot headshot.
On Star Killer base in the first section when defending, you have a very high vantage point over looking the first two objectives and is very easy to pop some heads that way if you can aim decently well. I was able to get 22-2 in one game with most of those kills being headshots. This game is quite easy to use these rifles as there is no moving or breathing when scoping. You still have to lead your shots but it isn't to bad. Just keep at it!