Grid 2 offers nine types of events that you have to complete and win. Most events consist of more than one race (i.e. Drift events contain three Drift races) and you don't have to win every single one of them as long as you have the overall highest score at the end of the event (first place gets 20 points, second 16, etc...). The only exception are Face Off and Touge events because they are based on elimination.
The first thing you want to do is go to the options menu and change the difficulty to the level that fits you the most. You can always change the difficulty to easy or even very easy if you struggle to win one event. I highly suggest you change the damage to visual only because the game has almost only tight and narrow tracks. Especially the japanese Face Off / Touge events can be deadly with high speed and sharp turns.
You don't have to complete the Vehicle Challenges for this achievement but I recommend you do it because every car handles different and even two cars with the same specs can act completely different on the track. Keep that in mind when choosing the proper car for each event! The Vehicle Challenges provide an insight into the different cars. Important Note: Vehicle Challenges are missable! Complete them as soon as possible if you want every car in the game. Don't go to the finals or another season before completing all Vehicle Challenges!
The cars are divided into three categories: Grip, Balanced and Drift. Choose a car based on the categorie and stats! I can't tell you which car is the best for which event because you have to try for yourself which car fits your driving style the most. I used grip cars for most race events, others prefer balanced ones and some might want to use drift cars (which are hard to handle during races).
Note: You can repeat or complete lost/missed races using the timeline. But it is easier and clearer to finish every Event and Promotion event before advancing to the finals of each season.
Event specific tips:
The standard Race events that we all know and love. The goal is to be at the first place after the given amount of laps or distance. The distance Races are way easier than the circuit ones. The Races in this game are very short (not longer than 4 - 5 minutes) but are not that easy because almost all tracks are very tight and offer only small place to overtake the other drivers without crashing. Unfortunately most tracks are unclear because of hills and the background setting. My advice is to keep one eye on the street and one eye on the minimap until you know the tracks. That should be easy because the game offers only a small amount of tracks. You get slowed down for a few seconds if you cut corners. You are allowed to use the side-strip on the racing circuits though. Use them to take corners while maintaining a high speed and ignore the narrator who'll tell you "this costs you a few seconds" every time because this is not true. Using the side-strip will be faster than slowing down.
Eliminator races work exactly the same way as in the DiRT games. You compete against 11 other drivers and after 20 seconds a countdown starts that eliminates a racer each 20 seconds. The last driver wins (after 4:20:00 minutes). Use the same tips as for races.
3. Time Attack:
Time attack events consist of three races with either 2 or 3 laps. The goal is to have the best lap time at the end of the race. Use the first lap to get used to the track and overtake the other drivers and try to improve your time on the following lap(s). It is easier to get a good time if you are first place because the AI drivers won't go into your way.
Checkpoint events are like Endurance events, but with a little twist. A countdown shows your remaining time and the race ends once the timer hits zero seconds. The driver who drove the longest distance wins. There are blue checkpoints (marked with signal flares - like the starting point) that give you between 3 and 11 seconds if you pass them. You have to drive through the checkpoint (it has the same width as the road) or you'll get a "checkpoint missed" message and your car gets reset which will cost you valuable seconds. Try to drive as clean as in Time Attack events and you'll win.
5. Face Off:
Face Off events are 1on1 events based on elimination. You have to win three Face Offs in a row to win the event. You get eliminated if you lose (but you can retry)! Trading paint is allowed. Drive dirty if you have to! The later Face Offs are on 8 - 10km long tracks. Don't use your rewinds after every small crash. You'll have plenty of time to get to your competitor and overtake him. I suggest using a grip based car because you'll face many tight streets and sharp corners. You'll have to keep a high speed in order to win.
Touge events are like Face Offs but only 2 races long and way worse! You get disqualified if you touch your competitor. This happens too if HE crashes into you! This is very unfair and it can be frustrating to restart an event for the fifth time just to see the AI driver ramming you to get you disqualified AGAIN! In Racedriver: Grid you were able to force your competitor to brake and let him bump into you to get a penalty. This is not possible in Grid 2 due to the diqualification rule! A special rule applies to Touge events: The "5 Seconds Rule" gives you an automatic win if you are more than 5 seconds ahead of your competitor.
Forget everything you know about the awarding of drifting points and multipliers you learned in Racedriver: Grid! This time things are completely different. It is much easier to gain high points but you can't keep a multiplier. There are red poles in corners that give you extrapoints and a multiplier if you drift past them. Points are based on speed and angle. One pole can give you a 2x or 3x multiplier. If you drift past 2 poles in one drift you can get a 4x or 5x multiplier. You can't "chain" drifts like in Racedriver: Grid. The points are added to your total once one drift ends. You won't get points for a drift if you either crash, hit the red pole and/or spin.
Overtake events are promotion events. The goal is to overtake pick up trucks while keeping a high multiplier. The multiplier resets if you drive off track, touch a car or crash into a wall, guardrail etc... The max. multiplier is 10x and gives you 1.000 points for each car you pass (you start at 100 points for each car). The multiplier slowly decreases if you don't overtake cars. Keep that in mind but don't let it stress you. It is better to lose a bit of the multiplier than to reset it completely!
Endurance events are like races but only appear as promotion events. You have to drive 5, 6 or 7 minutes and the driver with the highest distance within the time limit wins. The same tips as for Race and Eliminator events apply for Endurance events!
I hope that those tips help you to win every event!