Before the (" Combat Update" With the new damage stats) It was possible to get Overkill by using a Diamond Sword Sharpness V with Critical hit
Now even if you use an axe with sharpness V with Critical Hit it will only reach 16/20Damage instand of 18+/20(like before)

You should be able atleast to use a Sharpness V diamond axe while crital hit to get this achievement:
Just who really want Smite on his sword ._. . . .