(edit 14/08/19 - yes, you can simply enter then quit 2 and 3 star events (extreme-khana and buggy events included) to lower your driver level, thus lowering the opponent AI stage times. This is quicker than running rally stages and doing some overtime prior to crossing the finish line).
All of the other championships types seem fairly easy to win, but I was having a lot of trouble winning a rally championship, even after purchasing and upgrading several rally cars.
Thanks to robnitro on the racedepartment.com forums I seem to have found the issue...
Turns out that the game increases your driver level each time you win a race. Once you've put in 50 hours and increased your level to a fairly high standard, the AI times for the other racers in the 4 Star championships become difficult to beat (at least they were for me!)
I'd fully upgraded a Category 9 Citroen DS3 Rally, having read elsewhere that picking a car with the highest stability rating would help. This was a quick car, but I still could not win a 4 Star championship.
Decided then to fully upgrade a slower (but even more stable) Category 7 Citroen DS3 R5. I was having better luck with this car at first, but as I'd add each new upgrade the races seemed to becoming harder to win.
You may have noticed that you are offered higher level recruits for your team as you progress through the "career mode". I had a collection of Level 19 and Level 20 personnel on my team. If you purposely lose three or four events the level of the available recruits will begin to drop. Simply run any available 1 Star rallies, but don't cross the finish line until you've clocked up 30 seconds or more than the indicated Leader time. Go and check the newly available recruits and you'll notice their expertise level dropping.
I got mine down to Level 11, then forced a 4 Star Rally championship by entering and quitting 2 Star or 3 Star events (use 'Quit Activity' from the pause menu after the race has started).
If you're lucky you will have a 5-event championship available. If you want to run a 6-event championship then hopefully this method will still get you through. I'm not a fan of a couple of the locations because some seem to have quite uneven overall times set against them. And perfecting a sunset run through Monument Valley is just not fun when you can't even see where you're going! What I'm trying to say is just pick a championship that contains your favourite locations and get cracking. You should now find that you're having an easier time beating the AI times.
The five event championship I beat started with Japan, which can be tough to win due to all the 90 degree corners and tight village streets, but I came through and won it 6 seconds under time. The second event was a fun 12km run through Kenya, and even with three attempts the best I could do was 6th place. I decided to carry on and see what would happen. The third event was a long Malaysia run, and this one was pretty tight. I had to perfect the high speed sandy beach sections to keep the overall time down but won it by around 3 seconds. Sequoia was the fourth track and the times on this are ludicrously easy, I ran the track and beat it by 36 seconds! The final run was through Siberia, and thankfully the times for this one were quite comfortable to beat. Yay, achievement!
Forgot to add that I used the Category 7 Citroen for this run. You may find that switching on the TCS in the main menu may help improve your times also.
One last thing to add, I think you may be able to simply quit races to reduce your Level, I need to test this with a few DNFs and see if the recruit levels drop (see edit at the top).
Happy racing to you and hope this helps. Poops out!