Spectral Force 3

To recruit Chulcha, you need to complete the mission "The Trouble With Goblins".

Mission requirements: Attain the rank of Hired Mercenary.

Recruitment requirements: Do not attack Chulcha or her mother.

Once you have unlocked the mission, complete it without doing any damage to Chulcha or her mother (the goblin called Mama). You will begin the mission in the center of the map and surrounded by goblins. Chulcha will be behind you and will not move, so not attacking her is no problem. Mama will be in the last group of goblins that will move toward you. You will spot her because she is brown while all the rest are green. DO NOT do any damage to Mama, even collateral damage from exploding barrels, etc. Damaging either Chulcha or Mama will cause you to lose your chance to recruit Chulcha. Once you kill 10 goblins, the mission will end and Chulcha will join your group.

The achievement will unlock after you have saved your game.

Thanks to Albino Bob 325 for pointing out that it looks like you do not need High Mercenary rank for this achievement. I have edited the achievement requirements above.