Each event contains 5 challenges that you must complete. Some of these can be really tricky. The best way to go about this is complete the free roam story mode first. This will allow you to unlock the Hoonvan which i found to be the best car in the game. Its fast and drifts really easily. Most events have some simple challenges such as drift N times and perform 3 donuts.
Once you have completed the main free roam mode you should have cleared a large amount of the challenges and just be stuck with the hard ones. When you are working toward the difficult ones, dont bother trying to complete more than 1 in a single run. Focus on a single challenge for the duration of the run and you will find that it becomes much easier to complete this challenge when its the only thing you need to complete.