Everything you can learn yourself without a coach. If you are someone who thinks, 'well, no, you can't learn some of the things' -- as someone mentioned 'bridges' (not sure what he means). However, then how would someone like Paul Morphy, world champion be able to learn everything in the 1800s when there were few coaches and rarely many books (he was just genius, but also worked hard). How do you think he became so good?
Yes, you can learn everything yourself. It's just a matter of dedication and time spent. In addition, the adding of change to your games. In other words, if you continue to play the same style and the same openings/philosophies/strategies--you will be STUCK.
I know people who have been 1200 for years. I know those who have been 1300-1400 for years (including me :P). Yet, I have been able to improve myself, and now feel I am passing the 1400 barrier, by changing all my habits. Completely revamping my own thinking.
Watching more videos on chess (not on chess.com, mainly youtube), analyzing every single one of my games, even ones where I win (advice Kasparov once gave) for inaccuracies.
I have also learned NEW openings and tried them out.
Using tools at chess.com helps as well.
A coach would be very useful, but unfortunately, all coaches desire time, attention, and money---in addition, they make no guarantees of helping you---if you pay him and he turns out to be a horrible coach (you're screwed).
I use to have a friend ~1800, who use to play all the time with me, and try to coach me, but because of his immaturity he didn't know much about teaching. All he did was play me most of the time, beat me, and say I played bad. Or he would point out one mistake, but nothing to help me improve. He couldn't articulate his STRATEGY or TACTICS, or explain openings (so becareful, interview your coach first, let him give you one free lesson first).
I cannot say I have had a real coach myself. What I can say is, 99% of them suck. Even ones who are IM or GM. Have you seen videos by GMs, who cannot even begin to articulate their ideas (I know some people have, but I won't mention names of GMs)? Chess coaches are hard to find, and most of the time, they won't help you too much, because they don't have a strategy to improve your game.
So a coach wouldn't be wrong to at least mention the Luncea position for "homework."
Your rating will change depending how much effort you put in it.
Nicely stated