I did this solo on House - Hostage Rescue - with Thatcher (the character probably doesn't make that much difference other than the option of a flash bang to stun the bad guys).
You can limit the map and terrorist hunt game type in the second half of the matchmaking options.
Choose the construction site spawn point and run to the front of the house and to the right side. Repel up and melee the top double window and with any luck the hostage will be there. As soon as you knock out the first piece of barricade the game will tell you you've found the hostage and it may take a few tries to get the hostage here - they spawned here for me quite often. The room has some construction planks piled up in the center and will have 3 enemies - two in the front part of the room and another will enter at the back.
Take out the enemies whilst hanging there in the window and repel in. Grab the hostage and go back to the window and hold A to repel back out and up to the roof. Move across the roof towards the extraction point and enemies will be coming out in to the street. I took out the first 2 or 3 then headed to the right of the roof and repeled down the side to the garden, out of a gap in the wall and across the street. There's some steps leading down here and you can take this low path, then stay on the steps leading back up to the extraction point to finish the level and avoid the enemy fire.