(IT APPEARS THAT A GLITCH OCCURS AND SOMETIMES CHALLENGES DON'T COUNT, USE YOUR ACHIEVEMENT TRACKER AND MAKE SURE IT GOES UP AFTER EACH CHALLENGE)
Landing challenges are located under 'ACTIVITIES' on the welcome screen. There are a total of 24 challenges, 8 famous, 8 epic, and 8 strong wind. There are more flight challenges available if you download the 'World Updates', I'm unsure if you download these that you will have to complete the 'new' challenges also for the achievement, so I advise you to complete the challenges before downloading any of them. Let me know if you did download them and didn't have to complete them in the comments, I'll list out the base game challenges, as the game doesn't tell you.
It doesn't matter what you score on them, you just have to complete them. I advise you to complete flight training before doing anything in the game, it will make your life much easier. (I completed all the challenges with just the flight training, so I highly recommend it before even reading this guide.)
I'm not the best pilot and almost all these challenges only took me a few tries, with all of them only taking a few hours. Some tips I can give you is look at the 'flight plan' that shows up while loading, it shows you the speeds that you should be at and where the landing strip is, as you don't get a mini map in flight, sometimes it's better to scope out where the strip is and then just restart, that way you have a better way of planning out your landing.
Before landing you want to line your plane up as best as possible with the strip, using 'LT' and 'RT', and keep lowing yourself as low as possible, while lowing your power with 'B' and using the up and down arrows on the 'D-Pad' to adjust your flaps, these will slow you down. When coming into land you want to keep lowing your power by pressing 'B', I turn mine all the way down when I'm a few hundred feet away. Once off, I switch to holding 'X' and keeping my plane steady, don't use 'LT/RT' when about to land, as you have no speed and will crash. Let your plane gently go down by itself, once touched down, press left on your 'D-Pad', while still holding 'X', to turn on your parking brake, it's essential on the challenges with small strips.
If my text tips didn't help you, I'll link this video that gives some great tips on landing. Only thing I would change is the view, press the 'VIEW' button on your controller to change to the 3rd person view, unless you feel confident to land the plane from the inside, I honestly don't know why your reading this guide if you can.
All credit goes to "Squirrel" on YouTube. He also has some other tip videos that have helped me a lot through the game. Leave a comment if you have any other tips that have helped you.