This guide is pretty much meant for people trying to get this achievement without boosting.
The Hammer of Dawn is a somewhat difficult weapon to use since aiming it can be a little tricky and glitchy. Pretty much, you have to charge the beam for about three seconds before it fires. If the tracer beam is interrupted the countdown will reset. I would recommend not aiming the tracer beam directly at any target or, if they're moving around, near their feet. Try aiming the beam near structures or at something above them to prevent the Hammer from being interrupted.
Another thing to note: The Hammer's beam gradually gets weaker the longer the charge is held. After the initial blast (when the beam is a one-hit kill), let go of it and start anew. Since the Hammer has infinite charges, you will not have to worry about running out of ammo.
Another method you could try doing is downing an opponent (if you're bashing with the weapon, it takes three melee strikes to down instead of two), stepping back, and attacking them with the Hammer's beam. This is less effective on Execution than it is in Warzone. This achievement cannot be earned from kills in Annex.
Maps with the Hammer of Dawn:
A personal favorite of mine, Rooftops has two Hammer of Dawns (one just outside each spawn in a little hut). I found it very easy to gain kills on this map when I was able to play on it. The trick is to try aiming at corners and pipes above the enemies. It will be hard getting kills with this weapon in the middle of the map (Torque Bow). Another benefit about using the Hammer on this map is that it will be difficult for other players to try killing you right away (unless your opponents include someone who knows how to use the Hammer of this map).
Gardens (DLC Map):
This weapon is on either the middle left or middle right of the map (depending on what side you spawn on) near a tree. While I have not seen many people use the weapon this particular location is a popular killing zone. I often found it difficult to even use the Hammer of Dawn on this map. If you do get it, you'll have to beware of flanking players and for people using the Longshot.
The Hammer of Dawn is located in the middle of the map, between the Torque Bows and in the way of the train. If you're capable of getting the Hammer, it can be a very useful weapon on the map since there is little vertical cover (unless you're by grenades) and the map is small. If the enemy has Torque Bow, though, you will have a difficult time to using the weapon.
Out of all the maps this one is probably the most popular. The Hammer of Dawn is located in the building in the middle of the map. This weapon is handy since the map is large and open, and can even be used to blow up the gas tanks near the outdoor spawn (only once per match). The downside is that it spawns in a spot where it is very easy to get killed. Usually there is an enemy headed to this location as well and there is also an explosive gas canister by it which can be used against you.
If you do manage to get the Hammer, be mindful of snipers. You can use the weapon to flush out anyone in hiding unless they are inside the middle garage or inside the hangar spawn.