I was actually using the beginning of Downtown District (albeit on Rookie) to grind for 3x Frag Grenade, for Remote Explosion, inadvertently got myself EMP Stun, and especially for Last Known Position (though nott on the same run as a 3x Frag Grenade run). Here's how:
3x Frag Grenade or Remote Explosion: Head towards the middle entrance, then take cover against the wall while selecting the frag grenade -- once you get to the edge and turn the camera towards the room interior, wait a moment and then toss a frag grenade through the right doorway on the opposite side of the room. (You MAY have luck doing this with the left doorway, but I wouldn't count on it as much.) If you feel that a distraction device is needed first to "freeze" guys in place, toss an EMP grenade or flashbang (hence EMP Stun and/or Stunned) first. For Remote Explosion the enemies won't try to run away, but you'll need to be a little more careful with the mine's placement and time the detonation right.
Last Known Position: This one is actually quite simple: Crouch walk through the left entrance, staying behind the kitchen counter and wait for the guards to take their positions. When the guard around the corner (of the counter) turns around, get the melee takedown. Mark all three guys in the room, and if you have the Reflex Sight on your Five-seveN, pick someone still in the hallway on their side of the room. (Of course, if you didn't already get Sonar Mark, activate that mode first.) Go back into the theater, get yourself detected at the middle entrance, then immediately run back to the left entrance, crouch-walk back in, and execute -- on average you should get three kills or more. Retry Last Checkpoint so as to rinse and repeat.