Bring about 2 medics (heal wand holders) and 1 torcher (flame torch holder - worst creature-creature fighter) to a wild animal nest. Have your torcher attack the alpha ones, and leave the medics a little behind, but still in sight for the torcher.
The Chieftain will revive after a period of time if killed, unlike all other tribe members, so this is easiest done with the Chieftain.
The easier way to get this achievement is, after deal with all the other tribes, bring all your tribe members together in your tribe, and let time pass without giving them any commands, making sure there is about two healers there. Eventually, food will run out, and the tribe members will start to starve and lose health, and will be healed by the healers. After some minutes, the achievement will show up.