I am also having this kind of problem. My achievements that have problems are not the same as your but I have watched some chess TV, and still didn't get the achievement "TV guide". I also don't know how to link my facebook account in order to have the "friend me" achievement. I have read more than ten articles, but I didn't have the "reading glasses" achievement.
you have to become premium in order to have some achievements.
By the way, one of the achievements is to have 100 friends. Feel free to send me friend request, if you want to.
The new chess.com achievements are an interesting incentive to get people to explore the various features of the site. For example, I never would have known I could post this "forum topic" had it not been for the Conversation Starter achievement. However, I am still not very clear on how to earn the achievements. they do not seem to be consistently awarded. For example, Ballot Box is presumably awarded if you have played in a vote chess game. I have played in a vote chess game, but the achievement was not awarded. Likewise, Challenger is supposedly awarded for joining 100 tournaments, but I have joined well over 100 with no award given. Finger Paint is given for customizing your theme. I have but it wasn't. And there are quite a few other awards that I have not received even though I have met the criteria. Apparently there must be additional requirements to those listed, but there doesn't seem to be any clues anywhere to indicate what those requirements may be.