This is a lot easier than you think. Since there are only 4 characters you can do this almost right away,
For grabs walk up to a guy and hold B.
Melee kills walk up to a guy and bash B fast.
Signature kills wait until your special bar is filled up then walk up to a guy and it will you to hold X and it will zoom in on your kill.
Do those 3 things with all characters and you will have the achievement.