Hydrophobia

Here is a video guide (mind the intro) for this achievement. Soon as the timer starts run back to the chief and open the door behind him to put out the flames. Reload checkpoint if timer runs out.

Video credit: SamueltehG33k

After the bad guys leave and you enter the security room and use the terminal, you have to run back to the Chief in a set amount of time. On normal, I think it was 45 seconds, which is pretty tight. If you take a wrong turn or two, kill yourself so you can try again. The path is pretty straightforward and the only tricky part is the part where you have to climb past the fire - just immediately jump to the rail, wait for the fire to die down and then climb past. When you get to the chief, pop out your console thingy and look at the door behind him, through the glass (it'll be highlighted in green), then press X to open it. Water will flood the room and put out the fire, saving the Chief.

If you screw up, the Chief will beat the window of the office out and escape anyway, but you won't get the achievement. If this happens just run into some fire and die. You'll go right back to the start of the timed sequence so you can try again, even if you fully watch the cutscene (the checkpoint isn't until after you use the terminal in the Chief's room, I think).

On normal and/or hard difficulties, you'll have 45 seconds (otherwise 1 minute if you're playing on easy) to save Chief Billingham. Achievement pops if successful. If you fail, the chief will beat the office window and escape anyway, but the achievement will stay locked. If so, reload checkpoint and try again.