Achievements should not be game progress markers.
It’s disappointing to see “Achievement Unlocked!” only to find that the achievement was for beating the level. Beating the level tells me I beat the level. Achievements are supposed to medals for going above and beyond the call of duty. They should be true feats of gaming prowess. Progress should absolutely be marked—the player needs that feedback—but it should be a separate system from achievements.
Having formidable achievements to attain can add lots of replay value to a game. It sends the player back through the world with new eyes, yet the developer hasn’t made any new areas. Achievements will often evoke creative involvement by the player or even multiple players cooperating for one achiever’s success. Achievements will keep advanced players coming back to the same world.