Are you on xbox 1? If so, try changing your gamertag profile through the game, and then logging back in (this is different than switching characters). - Load up your character and get to orbit like normal, then press Start/Menu > Settings > Log Out > Switch Profile - A dash screen should appear to let you pick a gamertag. Select the same one, and you should be brought back to Destiny at the character select screen. - Now pick the same character you have unlocked the achievements with, and then wait a little bit once you get to orbit and see if any of the achievements pop. More info: https://www.bungie.net/en/Help/Article/12242