This achievement is for getting a win in each of the five game modes: Galaxy Assault, Star Fighter Assault, Strike, Blast and Heroes vs Villians.
Due to this achievement being a little buggy, please check your progress bar after each win. If your progress bar doesn't go up, get another win in that same game mode or come back to it later but make sure you know which game mode it didn't progress in and keep going for it. For me, it happened to be Starfighter Assault.
If that doesn't work, try getting wins in other game modes.