I'll tell you guys what I did.
First, I killed the two guys that run out at you (one from each side).
Then, I ran past the corridor (fast, so you don't get shot).
Hide behind the boxes, kill the 6 or 7 guys behind the boxes.
Now, get the 203 out. Peek so you can see down one of the corridors, but neither shooter can see you. Shoot the grenade, kill the shooter, than flip around and do the same to the other guy.
Now, you have to pick one side (you don't need to clear both sides). When you walk in, a guy runs in, kill him. There should be two guys in the next hall. I recommend the 203s and flashbangs for clearing the hallways and the next room.
When you get to the next room, another guy will run at you. Kill him.
Then, on the opposite side there will be two guys (who shoot really fast and accurate). Use the 203 to pick one off, and then shoot the other guy by barely peeking out.
You should see Price say to keep moving then you'll be clear to go.
You need to do all of this really fast and hopefully you get the checkpoint at the next part.
The hallway section took me two hours to find a strategy of how to clear it.