UPDATED 2016-09-12: Corrected some grammatical errors and whatnot.

This is no guide, just some general tips on how to beat the first part in Chapter 13. The part where Adams is down and you're alone with a lot of enemies.
What you should do is to go ahead and die once, and you should spawn behind some cover (You'll find yourself at the center of all the cover there is in this area). Walk left from that cover and there should be a single-shot rifle for you to pick up. Now walk right and pick up the grenades that should lay there. Now leave that cover and walk to the most eastern cover there is. It should be a narrow one where you can walk from left to right whenever the enemies try to frag you. Now just stay there in cover and
SAVE YOUR GRENADES.The enemies will fire at you, but since you're behind cover, they will miss. Now wait until you only have a minimum number of enemies shooting and you. Raise your head and try to shoot ONE enemy in the head at a time.
Don't try to kill multiple enemies at once as the chances of you getting killed are pretty big. You could most likely do it, but it will take both skill and luck.
When you've killed enough enemies you'll see two guys with masks coming towards you. With these two guys, there will be a heavy gunner. While they run towards you, exit your cover and rapidly fire multiple shots towards their heads. Try to get both of them, so you can prepare for the heavy gunner.
Once the heavy gunner comes closer, toss both of your grenades and keep firing your gun at him while remaining in cover as much as possible because this dude will shoot you dead. Once he's dead, you've made it passed one of the toughest - if not
the toughest - part in the game.