Well first off, if you have a lot of money to invest in a GM instructor you can surely go above 1600, but if you don't: don't let rating and score interfere. Starting a game and thinking about victory is not smart at all. Focus on your game-play instead.My friend (IM 2470) always says chess is 50% skill and 50% psychology. I see people here saying tactics, I'm going to tell you right away that is incorrect. For a decent 2000+ player you should work on all of your components:
-Have 2 openings with white and two with black - why? Because when you reach a certain level it's great to have a backup opening because your opponents will obviously prepare against you, and it's quite bad if you don't use the fact that you're white, just because your opponent has prepared for your always-the-same repertoire.
-Tactics-obviously an extremely important component, but, the point of working on your tactics is to remember different motives: you obviously won't have exact copies of the problems in your games, so motives are the ones who can help you greatly. That's why you need to use good tactics books with realistic problems, the ones that actually came from games.
-Work on what you're good at: many people say analyzing your games and looking for mistakes is smart, but, my short timed chess instructor taught me that you have to excel at a point in chess. E.g. if you're a positional player work on that! Make it even stronger!
-Discipline - every.single.day. if you just once say "I will skip today, but tomorrow I'll do double" it's all over, cause you're going to keep saying that again and again.
-Don't be picky with books- essentially any good recommended books will work, don't be like "I don't like this one so I won't do it."
-Work on all points of chess- for openings learn the plans and the moves (you won't figure them out by playing a lot, you have to learn them and then see if you can remember in-game), for endgames get a good books (I'd recommend Reuben Fine) and for middlegame- find a grandmaster who plays similarly to you(same openings, same style of play)- and analyze his/her games, I don't mean as in just go through them, but analyze them, figure out what each and every move is there for. :)