Players need to work on tactical pattern recognition and calculation. These are two sides of the same coin. We can't calculate very well unless we can also recognize the patterns on the chessboard.
My personal goal is to be able to either recognize or calculate 3 move tactics while playing speed chess. I think that there is a difference from 1500 to 2000 where the players go from calculating tactics to recognizing more of them instantly. Starting in the mid-1990s, I spent a great deal of time studying tactics and this took me from 1800 to 2000.
Many people claim that speed chess is bad, but I don't agree. It builds pattern recognition and teaches quick calculation, although it depends upon the person. Speed chess can create bad habits and some people just need more time to calculate.
There is this idea called "The Woodpecker Method" and a book by the same name. The method is to study the same set of a thousand tactical problems repeatedly. Each time you do them you will get faster at doing the entire set. Another author, Michael de La Maza, had the same idea in a book called "Rapid Chess Improvement". Before he wrote his book, he first published it as an article, but first, he sent the article to me to ask what I thought of it because I had already created a website advocating a similar idea.
I inadvertently discovered this method when I created my chess lesson website around 1996. The Internet was still very young and there wasn't much chess content so Chess Life magazine gave me an "award" for my site. After I spent months creating the 1, 2, and 3 move problems on my site, I challenged myself to see how long it would take me to go through each set of the white-to-move and black-to-move problems. It took a long time. However, the second and every subsequent pass was faster. I think that a 2000-level player should be able to get through each set of 1, 2, and 3 move problems in 30 minutes, but only after much practice. I have achieved this many times, but now I fall short so I intend to study the problems more.
I've been accused of just memorizing the answers to all my problems and not doing any actual tactical calculation. This is half right. For some problems, I remember the answers, but for others, I just remember the pattern involved and a few I don't remember at all. Even if the accusation were 100% correct, this would not be a bad thing. Chess skill relies on remembering what we have seen before and recognizing those patterns over the board.
Some people improve just by playing a ton of games, and this can work, but I think that it is less effective than studying tactics. Although most people play a great deal, I don't play many games and prefer to spend my time studying chess.
I also have thoughts on what it takes to become a chess master...
In the late 1970s, I studied basic King and Pawn endgames and became proficient at them. In the mid-1990s I studied more complex king and pawn endgames, all of which were from my games, and became skilled at those. I didn't have to memorize these endgames because I understood why the moves were correct. It is easier to retain information if you understand it, but this is harder to apply to other areas of the game like openings. I think that endgames are easy to learn, except the more difficult ones like the bishop and knight mate or the queen versus rook ending.
I have a full course covering King and Pawn Endings on my website.
My point is that I think that it is possible to take one small area of the game and master it. I have done this with King and Pawn Endgames. Chess is not just one skill, but many, so I think that a person could master chess by just focusing on one aspect of the game until they master it, and then move on to studying a different aspect of the game. For example, I think that it is possible to learn a particular opening as well as a master, although this would require much effort.
Online ratings mean very little to me. I can't control how well the anonymous person on the Internet plays or if they are cheating, which many of them do. What matters to me is how well I play. Likewise, losing games at the chess club doesn't phase me. I see losses as an opportunity to learn something. My goal is to always keep learning. Losing a game doesn't mean that I am a bad player, and I have confidence in my chess skill. I have no problem playing and losing to stronger players because my goal is to play the best that I am able regardless of the result.
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