This achievement is pretty straightforward. You must get 20 killstreaks while flying interceptors. You can do this in Starfighter Assault or Galactic Assault.
You get killstreak every time you shot down at least two enemy starfighters in one life (kills of both player and AI spacecrafts count, and I guess kills of ground troops do too, assists, on the other hand, do not). Next kill in said life is counted as another killstreak. That means you can get The Interceptor achievement as soon as your 21st kill. But there is no need for you to get all the kills in one sitting.
I was able to get the achievement in just one round of Starfighter Assault as the defender on Ryloth/Lucrehulk map (32 eliminations/23 kills). During the first phase stay between battleship arms near shield generators and shoot down every bomber you see and every fighter that is preoccupied with shield generators and doesn't pay enough attention to the opposition.
It's my first guide. Please let me know if there is something that needs to be corrected. And sorry for poor grammar and any grammatical errors. Happy hunting!