(1) You will be dealing exclusively with adult dog aliens on this level. In the entrance chamber with you when you start is a pulse rifle magazine. Grab it now because when the entrance door closes behind you there is no reopening it. Move forward, kill 3 adult dogs, and grab the derm patch.
(2) Move clockwise to the next pair of alcoves for another adult dog and 2 flame thrower canisters.
(3) At alcoves 3 are 2 derm patches and the exit doorway, but it's not time to leave just yet! Leave the exit door intact and you will only have to deal with the adult dog that pops up inside only once later on in this level.
(4) The next paired alcoves will be tough. As soon as you approach, you are attacked by a pair of adult dogs; at the same time, a second pair materializes back in alcoves 3 and attacks from behind you. If you back up carefully, you can see the behind-you pair of dogs materialize and can kill them first before activating the ahead-of-you pair. Pulse rifle (or smartgun) them all and move on, but make sure you find the 3 derm patches (1 of them is behind a hidden door in the recess on the right) before leaving the area.
(5) At alcoves 5 there lies a single pulse rifle magazine. You will be coming this way again, so grab it or leave it depending on your ammunition level.
(6) Continue clockwise all the way back to alcoves 1 where you started, obtaining the 2 derm patches lying en route. When you reach the entrance, you will have to eliminate 4 adult dogs (3 of which you previously killed) as well as a newly-materialized pair of adult dogs that attack from behind you in alcoves 8. Move carefully and you may be able to activate the behind-you dogs first and then the "revivors" (depending on where you dropped them earlier), making for a less dire situation.
(7) You will now have to make another full circuit of this level, killing all the revived enemies along with the new ones that were not present the first time around. There will be 1 new adult dog at alcoves 3 (remember to leave the exit door intact for now), and 2 adults each at alcoves 5 and 7 (in addition to any revived enemies). Don't leave behind the pulse rifle magazine in alcoves 5 if you didn't grab it earlier, and make sure you pick up the newly-materialized hypo pack in alcoves 4 and seismic charge in alcoves 6 your second time around.
(8) Keep moving clockwise until you arrive back at the exit door; you will have 1 new enemy here. Now open the door, kill the adult dog alien inside, and make your exit.