The Maul weapon is the sledgehammer. Below is a list of each enemy you need to kill with it.
Warrior- On the prologue level you will fight these and later on in the game as well.
Herald- You will see these enemies about 1/10th of the time compared to the warriors. They will be caring the heavier weapons such as the nano rifle.
Shiva-They a about a foot taller than the other cultists and are wearing some kind of mech armor.
Creeper-Average bug that melee's you.
Alpha Creeper-A bigger version of the creeper.
Ravager-These normally cling to walls and fire lasers at you.
Wraith-These go invisible with a white flash.
Berserker-These are the smaller behemoth's who explode when their health is about 1/3rd.
Behemoth-These are a bigger form of bersekers and are only introduced to you later on.
Monolith-These are the tower things that power the bugs up.
POD-These spawn the bugs.
I would recommend you copy this list onto a word document such as notepad and tick off each enemy as you kill them. You can find all the enemies you've killed on your Player Stats under the Extra option on the pause menu. Simply kill an enemy with the maul and see which kill stat has increased and tick that enemy off.
Note that the attack that kills the enemy has to be with the Maul. You can lower the enemies health and then Maul him, but make sure that the attack that killed the enemy is the Maul attack. I would recommend you go for this achievement on easy/normal to make it easier.
The super melee cheat will make this achievement easier, so if you're having trouble with the berserker or behemoth, that's always an option.