When completing a statue on the Easter Islanders Scenario, you will be given an option to choose an outcome/effect of erecting each statue. For imperfect statues, you must choose the option on the right at least once.
If you are trying to complete both this and perfect statues, I suggest you go for perfect statues first (by always choosing the option on the left, because they involve status improvements), saving the game before the sixth (second last) statue goes up, and then on the imperfect route, choose the right option after erecting the 6th statue. It has no status effect, so you are not disadvantaged by it.
Achievement will unlock once you have completed the scenario (erected the last statue).
For tips on how to complete the scenario in general, see the tips in the 'Perfect Statues' achievement.