The Inquisition Swords were added as part of the Betrayal DLC in Hardline. The Inquisition Swords are heavy melee weapons that take about 2 seconds for your character to swing. This means that if you think you can get a kill with the sword, you should preemptively start the melee action.
If you have not used the swords yet, try them out to get a feel on how long it would potentially take to get a kill with it.
The method I used, that worked, was to play Blood Money. A lot of people, when grabbing money from the objective, do not pay attention to see if they are going to get killed. They either lay prone on the objective, or they simply do not have enough time to react to threats. Depending on controller scheme, people are forced to use their right thumb to hold down the "X" button to pick up money from the objective. That means that they are unable to use their rightstick to turn while grabbing money and they have to adjust when they detect a threat. But in the time it takes them to react, it should give you enough time to finish them with the inquisition sword. Better yet, a very few amount of those people actually realize you are there at all. I have gotten up to a quad with the inquisition sword on Growhouse, its amazing how unaware people are.
The other half of the kills I got from simply watching the radar for stationary targets, such as snipers, and going out of my way to come up behind them.
With this achievement you have to be kind of risky if you don't want to use these swords for ever. Sometimes, you try to melee somebody and die for it and sometimes you get the kill. 50 kills isnt that much, but when it comes to getting melee kills, it can seem like a lot.
If there are any questions or concerns please let me know in the comments.