You cannot unlock this trophy until you reach Rank 13 in the online multiplayer.
Rank 3 - MP-443
Rank 4 - M1911.45
Rank 12 - MP-412
Rank 13 - M93R
The M9 handgun is your default handgun, you need to achieve 5 kills with each handgun you will know you've done this when you unlock the respective weapon efficiency pin. Once the fifth efficiency pin is unlocked with the M93R (if you did them in order) you will obtain this trophy.
This can be done in any game mode except for Onslaught.