People can easily manipulate Puzzle ratings intentionally or unintentionally and are a very weak indicator of chess prowess in general. I've seen players below 1500 Lichess ratings with 2200+ Puzzle ratings. It's not that uncommon to see players with Puzzle ratings hundreds of points higher than their game play ratings.
-Jordan
I'm a very very good example!😇
currently my puzzle rate is 2270 while my rapid rate is only 1573.
So it seems like that I have a clever mind enough to be a show-off while my brain got scrambled by the lack of time in games.
If you want a high puzzle rating, just take your time. I'm 2274 bullet (but have only played unrated for years, so that might not be accurate) & about 2700 puzzle. (That's why Puzzle Rush is better I guess, because it takes speed into account.)
Actually the biggest hurdle(for me anyway) is self-discipline. You try to go through all the possibilities and you lose track and it's really tempting to say "oh, I bet it's this, let's just take a shot". If you want a high rating you have to resist this.
I find the easiest is "Mate in 2,3,4", because it's a fixed goal, and there's only a limited number of patterns. I've done hundreds of them and I've seen most of the patterns. Of course if you're 2600 and you're doing mate in 4, you gain 1 for a success and lose about 25 for a failure, so you have to be really consistent, but I still find that easier. Endgames are hardest by far for me. (King+pawn endgames especially, because you have to calculate about 50 moves ahead.)
It's tempting to just do what you're good at, if you want to increase ratings, but I guess the whole point is to do what you're BAD at. You have to accept you'll lose loads of rating in the short term.