Note: This has to be done in consecutively without getting off a horse.
First call your horse or mount a random horse. Then you must find a Guard on another horse and press to assassinate him. You must repeat this four more times. If you get pulled off your horse or fall off somehow you have to start from the beginning. It is easier to find guards with horses in the Antico District.
Alternatively, the fastest way is probably to do the assassination mission Serf's Turf. You have six guards on horses right there. Start by the one who is alone when he is near the cliff as you won't get detected. Then go for the two together. Wait until the three guys are far and kill them both quickly.
You should now be undetected again. Now kill one of the three remaining. Both the others should become alerted. Just go close to one and assassinate. Be careful as one of the guards might get down off his horse and try to pull you down. Even if you have to replay the mission the starting point is really close.
Note: If you haven't done the Assassination Contract Serf's Turf, it is in the Campagna District North West. It is the one that is farthest up on the map in the first set you do.