By playing through the campaign, you will likely already have a number of these. I myself had 58/100 after completing the game.
A good spot (IMO) for farming any remaining kills needed is on the second (first after the prologue) level, Schöneberg Convoy.
Get to the room you remember from the demo (which you get to after killing the first three enemies and has a enemy with his back turned to you in it, with the German leaning against the doorway down the street). Move downstairs and position yourself against the window directly to the right of the exit door (if you were looking at it from outside, left from your perspective). There will be a number of Germans down the street. Fire off a shot, and they will scramble for cover.
On the right hand side at the end of the street there will be a lamppost with a car just behind a pile of rubble, with what looks like a wooden dresser to the right of the car. Germans will take cover behind this dresser, then will move out and start running down the street towards you, giving you an easy moving kill. Once you get better at leading enemies, you can get more from the Germans running across the street perpendicular to you.
Once you kill all but one or two Germans two more will spawn directly beside the car and take cover in the same spots. I found I could get 4-6 moving kills every three minutes or so. Just keep reloading the checkpoint after you kill all the Germans and repeat until you have 100 moving kills.
Be aware there is a sniper at the far end of the street and an MG42 in the building directly across from you. Obviously this is easiest on Rookie mode. Additionally, there is an explosive barrel at the end of the road, so feel free to shoot it before reloading to work towards Detonator.
Finally, this game does not track the kills in a logical fashion - some kills tagged 'Kill' (because you did not get a killcam shot on a moving target) do in fact count. I know this as I was keeping track and got 75/100 when I only had 69 on the tally. So just keep at it. If you really need to know, just quit out, check your stats and continue from the checkpoint.
Good Luck!
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