Firstly, not every puzzle in the categories are going to be the same in difficulty. There are Extreme puzzles that are extremely linear and can be solved in 2 seconds like an easy puzzle because all the monsters are crowded in two floors. There are Hard puzzles that have taken me a lot more calculation to find the first confirmed spot for a character than it took to solve most Extreme puzzles. So I advise you to not aim to "be good at difficulty X in puzzle type Y" but just "be good in puzzle type Y" specifically. Complexity does not always make a puzzle more difficult.
In birds, each bird is in a unique spot and each spot has a bird, so if you know that any spot cannot house two specific birds, then it means any of the other four birds can sit there. Generally that provides a vector of attack because if you find eliminations for three then you've solved it for it being the 4th. Generally these hints - "X is here" or "X is not here" is going to narrow down your solution space the most. It is followed by "far left or right" (and its inverse) because you know the solution is for board state X????? or ?????X so if you solve for one and you find it's a dead end you know the other pattern has to be true (logic through abduction helps - you should be able to assume which pattern is more likely based on skimming the other clues and with enough experience your first try to approach the most narrow solution space should be the right one). That leaves the final hint types: "X is adjacent to Y" (which creates 10 patterns: XY???? ?XY??? ??XY?? ???XY? ????XY and the flipped version) and its inverse (|x-y|>1, |y-x|>1, (x,y) in {(1|6,[34[56|12]]), (2|5,[456|123]), (3|4,16[5|2])}) and the hint that "X is to the left of Y" (or "Y is to the right of X"). Sometimes the hints stack and X is adjacent and next to Y, so you can get a quick optimization into X+1=Y or (x,y) is (x,x+1).
Jungle is probably the easiest puzzle type for me. 6 monsters take up one of the 8 spots so 2 will be open. If at any point you have enough information to know where the two open spots are (For example, only one monster in forest = two open spots in forest), then you are basically doing a Birds puzzle with more geometrical hints that narrow down the solution space much faster. If you cannot, generally jungle puzzles are easily solved (especially in Extreme since the complexity feeds into the solving process) by divide and conquer. If you see three hints around where the Tiger is and is not, then calculate all lines for all positions of the Tiger and it will likely bring you closer to the solution. If you are in a puzzle where each icon appears no more than twice, then you can procedurally "ignore" batches of hints and use uniqueness (the implicit rule that there is only one specific arrangement to solve the puzzle) and approach the solution by finding sets of potential solutions and know that the only set you should put more energy on is the one where the withheld batch of hints during the "ignore" can eliminate the solution space into a precise answer. There will only be one, so it will be the right answer.
In hotels, each monster is in a floor and they do not affect each other, so it's easiest to consider 6 variables each in the range of 1..4. Some problems will give you very generous hints like grouping monsters 3 together or telling you that X=Y+1 and also X=Z+1, so you are fed the information that you can consider the puzzle as the three monsters in a group and the other three monsters individually, essentially only having 4 moving pieces now. With enough practice these puzzles should be solved instantly the moment you look at them just like with very little mental maths you should know that 125x8 is 1000. Like with mental maths, your goal is to solve with as little effort as possible by solving smart, not that you should be working harder.
If you know that X<Y and Y<Z, then you have the following possibilities: X=1..2, Y=2..3, Z=3..4. If another hint happens to tell you where any of them are not in you can narrow that space down by 4 times immediately.
If you know that any of the center floors are empty (X≠2,Y≠2,Z≠2,W≠2,V≠2,U≠2 or the 3 counterpart), then all hints of X=Y+1 will immediately solve their positions because unlike the X<Y version, the hint locks them into the only two floors that can have monsters adjacent to each other. These are not the only tricks to find quick solutions and I'm sure you will come across a few on your own but they are patterns you have to develop through experience because ideally recognizing the pattern is already too late. You should be able to see hints that intuitively create a thin solution space and have it solved in your head before the pattern forms. Some of them are going to be messy and the structure would be across multiple hints (One of the Extreme puzzles I remember having five hints on the blue monster, a hint says he's not on floor 1, another says he's not on floor 3, another says he's not with red and all that jazz. Paired with another hint it's immediately clear he's on floor 2) but because the model is just six numbers you should be not afraid to brute force or guess once in a while if you do not find a good approach. Until you learn enough to find a plan of attack for most patterns you are going to have to guess a puzzle once in a while until the solution is obvious to you. When most solutions are obvious to you you will know how to solve them.
Because not every puzzle is the same, you should not expect all puzzles to have the same optimal routes to finding the solution. This is where experience in logic puzzles will help. I have participated in competitive sudoku competitions in the past and I used mostly vector maths, the same as I do for gammelogic. Instead of trying to win every game and skipping to the next when the puzzle is too hard I would recommend looking through failed puzzles you could not solve and had to give up / guess, and study how much the solution space changes when you apply different hints in different orders.
For example, in sudoku, my favourite technique is the Skyscraper. But to understand it, you have to know what X-chains are, then XY-chains, and these techniques build up to the knowledge that parity helps you find eliminations. If a grid is 1 or 2, and there is an immediately connecting grid that is also 1 or 2, and these rows, columns or boxes wrap around so that after exactly an even number of connections (so coloring them alternatively would result in two different colors from head to tail) both cells see a distant cell, that cell cannot be the numbers being repeated. When you build foundations in little bits of knowledge like this, you could practically recreate these techniques on your own. No matter what shape it comes into, the tools you have prepared will always solve a puzzle faster than guessing when the tools are applied in the right way. So get practice and find more tools you have inside you. I would even suggest that you don't just practice on hard puzzles - just like practicing mental maths, the goal is to be fluent and spend as little energy getting from the problem to solution as possible, so if you get to the point where you can solve Easy puzzles instantly, that experience will help you craft better tools to crack Hard+ based on what you know you can immediately solve.
