A good spot to nab this achievement is during the mission Bump in the Night. While playing as Preacher, you will exit onto the deck of a ship with an enemy standing in front of you facing the water. Hack him up and then turn to the right where you will see another enemy. After executing him, go around the far corner where another enemy should be standing. Directly behind him there should be one last enemy.
If done correctly you should easily be able to nab 4 axe kills at one time. Then just reload the checkpoint, rinse and repeat.