Go through this door and shoot the guard and the Super SS coming out of the second door to the left.

Now pull out your missile launcher, take up position in front of this door, open it and keep throwing missiles into the corridor. Feed them to them.

Then go down the corridor avoiding the poison puddles. Hopefully you will have a missile or plasma for the guard hiding around the corner, or else you will have to kill him with your knife. You will notice the brass key in the little room behind the wooden barrel.

Enter the southern corridor and locate this unlocked door. Take the axe within.

Continue.