Escape Dead Island

For this achievement, you need to get 10 stealth kills in a row without getting spotted.

I recommend doing this on Mission 6 - Stories of the Dead. You'll reach a point where you need to ride a cargo elevator up. Surprisingly, the ride get's interrupted, and zombies drop from the ceiling.

There's a check point right before the elevator ride, so if things go south, just exit and continue. Or alternatively, let yourself get killed and respawn.

There'll be exactly 10 zombies, the required amount for the achievement. When a zombie is about to fall, some green pus / ooze will preceed him, so look out for these streams and sneak over (never walk or run) to kill him fast. If you can't get him straight away (likely once several zombies drop at once), remain patient and hidden while waiting for an the right moment to approach your next target from behind.

The zombies come in waves, and drop roughly in the same spot each time. It'll likely take a few tries, but is by no means impossible for the patient stalker.

I just got this VERY early in the game (before completing mission 5). It does not appear to be as difficult as it would seem.

In Mission 4, I stealth killed three zombies BEFORE I reached the landing strip. Once there, there is a scripted event wherein you fight at least 8 zombies, and all of them detected me - I got zero stealth kills during this fight. After some story stuff, I continued to explore the island. After seven more stealth kills, the achievement popped. I'm certain that I had been detected by a zombie I was attempting to sneak up on that I then killed in open combat in the midst of those seven successful stealth kills.

Not once did I botch a stealth kill and then hide away and try again; whenever I botched a stealth kill, I killed the zombie by normal means (melee/pistol) and continued on.

The key appears to be killing 10 straight zombies that never detect you - Zombies that DO detect you (exclamation point fills red) can still be killed with standard attacks without resetting your undetected-stealkth-kill streak, but if you hide and then try to stealth-kill them after they've detected you, it kills your streak.

Thus it appears that the achievement should read "Get 10 consecutive stealth kills without the target detecting you before you stealth kill it."

It would be great if someone could confirm this though; this is only a theory supported by my experience.

It's the easiest in the prologue. After "stealth kill" is introduced you can get it by the time you get the keycard.
After given kill and walkie talkie moment. Let zombie come up, rush and katana him. Rush to dead-alive zom and katana kill. Once the zom comes out the wall stealth kill. That's four kills. The next room, stealth the one feeding then the first of the two that noticed you first, then the other. Sneak around and ice the fourth one in the room. That's eight down. Open door to the right in the corner with the main door. Two zombies you can stealth kill.
Achievement earned.
If you happen to die that initial zombie kill will not count(checkpoint-save happens after kill). After the above. Open the following door, just sneak to the zom ahead banging next to keycard zom feeding and stealth kill them both due that there are two zombies in the next room feeding with no door.