Although the achievement description for this says that you need all crowns in a world, you in fact need to get a crown on every stage of every world, which amounts to a total of 110 stages. That being said, this is the most difficult achievement in the game and the one which requires the most time.
To get a crown on a stage you must collect all bananas on it, without falling off or running out of time. This is extremely difficult on some levels and so it is recommended that you use practice mode until you are sure you can get the crown in as few attempts as possible.
The most annoying thing about getting crowns is that the stages are in sets of 10, and you must complete each stage to move on to the next. This means that, for example, if you only need a crown on the 10th stage of a set then you must complete the first 9 stages, collect all of the bananas in the 10th and pass through the goal without falling off or running out of time. If you don’t then you have to reach that stage again for another first attempt. However, a slight workaround that I found was that if you need a crown on a stage but fail on your first attempt, you can keep falling off the level until you lose all of your lives. It then gives an option of using one of five continues. By using a continue you get another first attempt at that level. If you fail again, repeat the process. Not only do you then technically have 6 attempts at a stage, but you can also practice it with the lives you need to lose. You don’t need to worry about using the continues either as you get them back every time you start a new set.
The 5th stage of each set is a bonus level where you must collect 25 bananas within the time limit to get a crown. These stages cannot be failed and so if you run out of time or fall off before collecting all of the bananas then you must complete the previous four stages again to reach it. This also means that the continue trick does not work on bonus levels.
After achieving a crown on every stage of a set of you will unlock a hidden stage. You must also get a crown on each of these hidden stages for the achievement. They are not necessarily more difficult than some of the normal stages, although I found the first and last ones took the most time to get a crown on. If you fail to get a crown on a hidden stage then you can use the continue trick, but if you run out of tries you must go through the whole set again to reach it.
There was previously a trick where if you hit the windows button you could resume your game as a first attempt, keeping all of your bananas and so making it much easier to get a crown on every stage. However, the game has been patched so that this no longer works which also means if you quit the game for any reason, whether it is accidental or intentional, you will have to start a set again.
The only real tips that I can give are to persevere and stay calm. Trying to get this achievement can get very annoying, so if you find yourself getting frustrated then take a break. Trying to play when frustrated will only lead you to rush levels and fall off, which leads to another tip: take your time. There are only a few stages in which you must go quickly to collect all of the bananas and reach the goal in the time limit. Try every level going slow and if you find you run out of time then you know the technique, you just need to speed up. There are some stages which may seem impossible at first but I can assure you that they are not. If you come across an awkward ramp with twists and turns, remember how the tutorial said to hold your phone and move slowly. For stages that have moving platforms, concentrate on staying on the platform rather than getting any bananas and once you have a decent balance you can collect them. Most important of all is to stay in control. One sudden movement of your phone will cause the ball to jerk and move too fast, making you quickly turn the other way and the majority of the time will cause you to fall off.