What the achievement asks
Rescue fifteen of the twenty-five explorers stranded on Island Expeditions. Ten points, account-wide.
Note the verb. These are rescues, not kills, and the in-game criteria are misleading enough about it that people have spent runs killing the very people they were meant to save.
Buy the spyglass first
The explorers appear as bonus objectives, a yellow mark on the map, and finding them by wandering is slow.
The Engineered Spyglass solves this outright: using it marks any rescuable explorer on your map. It is sold by the vendor aboard the ship before the expedition starts, Lieutenant Elda for Alliance or Provisioner Burg for Horde.
The ship vendor rotates weekly. If neither name is aboard, someone else is, selling something else, and the spyglass will not be available that week. Buy several when you can.
How you actually rescue them
There is no single interaction, which is why people stand next to an explorer wondering what to do.
- Some are wounded and simply need healing back up.
- Some are trapped and need to be clicked directly.
- If neither works, look around for an object beside them: a cure, a shovel, a pickaxe. Click that first, then click the explorer.
Once one is saved, the bonus objective completes and the criterion ticks.
Running solo, you can check the map as soon as you land. If there is no explorer on it, nothing on that island will move this achievement, and leaving straight away costs less than finishing.