Assassin's Run is an action challenge. The objective here is to get all the way through the level while killing all of your targets with a giant crossbow. There are civilians in the mix, though, and if you kill a civilian you will lose the challenge. However, you will want to make your way through the level as quickly as possible, meaning you should favor a mixture of accuracy and speed. The game's auto-aim comes in handy here, so use it liberally.
You'll begin in a small entryway with the crossbow out and ready to go, equipped with infinite ammo. Head outside as quickly as you can, wasting no time in lining up some kills. Three enemies will be in the first room. Kill them in quick succession with headshots. The next two enemies will be just down the hall. Kill them similarly. Head to the door ahead and it will be either locked or unlocked. If the light is green, it's unlocked; if it's red, it's locked, and you need to double back and kill remaining enemies in the room, marked by skulls.
Behind the door, you'll find three more enemies and a civilian in white and a mask. Kill the enemies, but avoid the civilian. As the last enemy falls, the door straight across from the entrance will pop open. Head through and into the next room. Pause for a second here. In just a second, a large wave of enemies will rush you from inside of the room. A civilian will be in the midst of the enemies, though. Zoom in with the crossbow, and wait for the enemies to come at you single file to take them out one by one.
Head to the right and up the wooden ramp and through the doorway to the next level. Youw ill come upon three open doors. The left-hand door houses one enemy. The middle door contains a civilian, so don't even bother with it. The right-hand door contains one more enemy. Quickly look left to right and pop off two headshots before the enemies can even leave the rooms. Now, use Blink to reach the door overhead.
As you reach the next room, the windows will spring open. Two enemies will await you at long range. One of them will be holding a hostage. Zoom in with your crossbow and pull off a headshot on the captor, and then quickly look to the stairway on your right. The other enemy will be coming up the stairs. Kill him before he realizes what's happening, and then rush into the next room. This room only has two enemies in it, so quickly take them out and head into the next room. This will be the last room, with enemies on the first and second floor. Look up and kill the enemies overhead, but several will teleport to the ground floor to take you on. Finish them off, and a white room will open. Rush inside and the challenge will end.