But I don't know how I can 'push' story mission achievements
Make sure to log into each of your characters. Only will the story missions and other achievements be "pushed" if you log into that character.
Make sure that you have all the datacrons for an achievement on one character. The achievement does not track the datacrons across characters. Also, make sure to log in on that character.
EDIT: All the datacrons for one side for a planet. For example, on Balmorra, you must get all the Republic Datacrons on a Republic toon to unlock the Republic version of the achievement. Tatooine will give the achievement if you only get one of the Cunning datacrons in the bases, since you cannot go into the other faction's base.
EDIT 2: You may need to play for an hour or go to a new location for them to log.