Escape Dead Island

First of all I can confirm that the Shadow Zombie kills do count towards this and all other kill Achievements. I know this because it's how got the achievement for killing a Bouncer in Mid Air.

After my second play through and into my third I got extremely annoyed with "Oh Shut Up!" as I am sure many others have as well. I had killed the first Screamer on the Tennis Courts (while it was screaming) after about 50 or so times. For me the unpredictability of the screamer really ticked me off. For instance it kept running at the balcony and then screaming when I was out of sight. Or it sometimes ran up the opposite side of the building as if it was trying to escape. After all that I was not looking forward to going through the Labs again for a third time in order to try and kill the Screamers on the way to the Marina again. So I desperately tried in vain to get the Tennis court screamer to respawn. I tried leaving the area and coming back. Nothing worked so I gave up. I played on through to the point where Devan runs off to the Marina and Cliff says his Keycard to the Labs says Devan is wrong. Made my way down the Mountain and into the area with the bodies. I didn't go towards the Labs and thus never saw the flash of lightning and screamer spawn at the broken fence like you normally would. Instead I headed back towards the helipad entrance. I noticed a screamer on the Ledge with the GeoPharm File. The one you can not reach without a grapple hook, which I didn't have at that time. Opened fire and killed it as it screamed. I was so pumped by yet another kill that I desperately wanted to SAVE my game so I wouldn't die and lose that kill. So I headed right back up the mountain to the top. It didn't save. Disappointing... but this is where it gets good. I went back down and low and behold the screamer had RESPAWNED! So I killed it again while it was screaming. I was so pumped by this I accidentally activated the Flash and the other screamer that spawns near the broken fence. Killed it while screaming... barely. And my Achievement popped! In order to test the RESPAWNING SCREAMER I went through the area towards the Labs and then turned around and came back. There he was again sitting pretty on the ledge. So... In short there is one screamer that Respawns over and over and over again. Use it to get this annoying Achievement!!

I can confirm that kills for this achievement carry over to your second playthrough. I killed two Sirens during my first run of the game, then killed three more when making a return trip to the Marina (after grabbing the gas mask).

Regardless, you should do your best to kill the first Siren you encounter while it is screaming. You have enough time to kill it before other zombies swarm you, and Sirens only seem to scream while there are enemies to summon. As such, this achievement does require some timing.

The easiest section for finishing off this achievement is found on your way to the Marina. The route is just past the caves that require some crouch-walking, after you go through a hole in a wooden fence. For further reference, the area contains a bunker with a locked door, the entrance to the Geopharm Labs, and a gas-filled tunnel that leads you to the Marina. Also, getting this achievement early requires the silenced pistol, which you can find in the Geopharm Labs. Using your shotgun will draw another Siren's attention, who may exhaust its screams while you are dealing with other fodder. Make sure to search every nook for more pistol ammo.

Anyway, you will come across two Sirens up on a hill after coming out of the caves, before you get to the Geopharm Labs entrance. Hide behind the first knee-high rock and put a couple silent headshots into the first Siren. Although it will scream, it will not draw additional enemies because it cannot see you. Once the Siren's health is low enough, wait for it to scream again, then spam pistol bullets until it drops dead. Repeat the process with the next Siren on the hill. The route will then split, where the left path leads to a bunker, the middle leads to the Geopharm Labs, and the right leads to a gas-filled tunnel. The final Siren in the area is guarding the right path.

Note: If you do alert the Sirens and get killed, you should spawn back at the cave exit where you enter the area. However, due to the long respawn animation, you will spawn out in the open in plain view of the first Siren. If this happens, quit the game and continue. You will spawn back at the cave exit, but you will have time to get behind the rock in front of you before alerting the Siren to your presence.

Also note: Those three Sirens may only spawn during New Game+, but I have already done the best I can to wipe this game from my memory. In addition, I do not know if the shadow Sirens count toward the achievement, but at least eight or nine normal ones will spawn throughout the New Game+ campaign, so there is still room for error here.

Edit: After reading several comments, it seems several people have run into zombies after the first Siren screams, even though I encountered none (since the Siren's alert meter did not fill all the way) while repeatedly trying to kill all three Sirens in one run. I am not above ruling this method as a glitch, but just know this is the best location I found for knocking out the achievement quickly.